Space Form Research Articles

THE EMERGENCE OF SECONDARY URBAN CENTERS OR THE WITHDRAWAL OF URBAN CENTRALITY TO THE SUBURBS: A CASE STUDY OF THE CITY OF TÉBESSA IN THE FAR EAST OF ALGERIA

Major Algerian cities have witnessed significant dynamics, causing radical functional transformations that impacted city centers and their suburbs, leading to changes in the traditional image of cities. This resulted in a new distribution of urban functions and a redefinition of the concept of "space." Consequently, the current expansion and extension of cities' urban structure has encouraged a new relationship between the center and suburb, where new points of attraction have emerged on the "margins and suburbs," resulting in "**new centralities**" that caused major transformations affecting urban communities, spaces, and functions. The city of Tébessa, like other cities and being a border city and transit area to the Tunisian border, has experienced a new form of urban spaces. It previously had a traditional urban centrality around the Byzantine wall, one of the city's landmarks, which dominated for a long time as a central point over the rest of the urban space (the center). However, in recent years, it has undergone major transformations, characterized by strong attraction of functions, activities, and services, especially commercial activity in some city neighborhoods such as Skanska district, Constantine Road district, and Annaba Road district, in addition to “La Rocade” district, which plays a fundamental role in drawing a new image of centralities within Tébessa city at present. Therefore, this modest research was primarily based on fieldwork through a survey of residents in the four mentioned neighborhoods and the use of field observation through an observation network of service and commercial activities within the urban space concerned by the study. Thus, attempting to show whether there are signs of emergence of new urban centrality models that have gradually begun to take their place in Tébessa city, which is characterized by functional and economic diversity (in the city suburbs).

Studying Fascism transculturally: Italian scholarship in the international arena

In 2005, Enzo Traverso argued that a very problematic trend was affecting German memory culture and scholarship about Nazism. Echoing an alarm raised earlier by Timothy Mason, the scholar contended that at least since the 1980s there had been a progressive ‘disparition de la notion de “fascism” du champ historiographique’ (disappearance of the concept of ‘fascism’ from historiography) (p.94). The phenomenon observed by Traverso has found concrete materialisation in the EU's politics of memory developed throughout the twenty-first century. As Filippo Focardi argues in his work Nel cantiere della memoria (2020), the EU memory discourse has been shaped around a totalitarian paradigm centred on the memorialisation of Nazi and Communist crimes, in which the notion of a general form of fascism finds little space, and Italian Fascism only exists as a marginal epiphenomenon. This situation has begun to change in recent years as the growing success of far-right movements across the globe has brought international attention to the concept of fascism. Many Italian scholars, who have never ceased to study fascism, are now directing their efforts towards the international arena to contribute to a discussion that seems to have acquired particular significance for the understanding of our time.

Matching Trees to Streets by Street Type: A Case Study of Street Tree Suitability and Services in a Highly Urbanized City

Street trees are a representative form of urban green space that play an important role in mitigating the environmental impact of urbanization. Planting the right tree in the right place in urban streetscapes can improve tree health and ecosystem services. Here, we propose a novel approach to selecting appropriate street trees using street type classifications. In the highly urbanized area of Uijeongbu City, South Korea, 221.9 km of streets with 19,717 street trees were classified into 12 types based on road width, aspect ratio, land use, and the presence of power lines. Appropriate tree species were selected for each street type, taking into account tree traits and functions as well as street environments. Then, we analyzed the structure and ecosystem-regulating services of street trees by type, also comparing the services of appropriate and non-appropriate trees. As a result, all 12 street types were identified, but their distribution was uneven. Tree dimension was the key factor in determining appropriate species, and, for the second most common street type, characterized by narrow roads, low aspect ratios, and power lines, only four appropriate species were identified, indicating an urgent need for more options. Additionally, the most dominant species accounted for over 20%, averaging 44% across the 12 street types, further highlighting the necessity of introducing more diverse tree species. Overall, appropriate street trees generally provided higher service efficiency compared to non-appropriate trees across four ecosystem regulating services. These findings emphasize the need for policies and guidelines that promote street tree diversity and enhance the ecological benefits of street trees. This study provides a foundation for developing sustainable street tree management strategies that contribute to healthier and more resilient urban streetscapes.

On weakly Einstein submanifolds in space forms satisfying certain equalities

We classify weakly Einstein submanifolds in space forms that satisfy Chen's equality. We also give a classification of weakly Einstein hypersurfaces in space forms that satisfy the semisymmetric condition. In addition, we discuss some characterizations of weakly Einstein submanifolds in space forms whose normal connection is flat.

The Sasakian statistical structures of constant ϕ-sectional curvature on Sasakian space forms

In this paper, we investigate the Sasakian statistical structures of constant ϕ-sectional curvature based on Sasakian space forms. We obtain the classification of this kind of Sasakian statistical structures. Our classification results show that the Sasakian statistical structures of constant ϕ-sectional curvature on a Sasakian space form with dimension higher than 3 must be almost-trivial; on a 3-dimensional Sasakian space form, in addition to the almost-trivial Sasakian statistical structure, there exist other Sasakian statistical structures which satisfy the constant ϕ-sectional curvature condition. We also point out that a rigidity result for cosymplectic statistical structures of constant ϕ-sectional curvature on 3-dimensional cosymplectic space forms in [11] can be improved to the corresponding classification result.

Hemi-Slant Submanifolds of Lorentzian Kenmotsu Space Forms

In this paper, we study curvature properties of hemi-slant submanifolds of Lorentzian Kenmotsu space forms. We define Lorentz Kenmotsu space forms and study their curvature properties. We give example for hemi-slant submanifold of Lorentzian Kenmotsu space forms. Finally, the curvature properties of distributions are analyzed and the conditions for Einstein are investigated.

Lagrangian H-umbilical submanifolds in complex space forms and pseudo-parallel cubic form

Lagrangian H-umbilical submanifolds in complex space forms and pseudo-parallel cubic form

Biharmonic slant submanifolds in space forms

In this research work, bi-harmonic slant sub-manifolds in space forms have been studied. Bi-harmonic maps are critical points of the bi-energy functional and are of great importance due to both analytical and geometrical characteristics. After the study of Riemannian Manifolds with complex and contact structure and s-space form structure along with slant sub-manifolds theory, some significant developments related to bi-harmonic slant submanifolds in space forms have been established. Manifolds with constant sectional curvature is known as space form. As s-space form is the generalization of complex and contact structure, we get generalized results. Different aspects of results have discussed.

Biconservative hypersurfaces with constant scalar curvature in space forms

Biconservative hypersurfaces with constant scalar curvature in space forms

Assessment of Ventilation Performance and Thermal Comfort in Semi-open Spaces of Naturally Ventilated Traditional Dwellings in Tai Lake Area, China

Semi-open space is a special architectural space form between indoor and outdoor, which has the functions of transition, climate regulation and energy saving. Effective use of semi-open space is an important ecological strategy in adapting to the climatic conditions of traditional dwellings in Tai Lake region of China. However, it has been shown that the hot and humid summers in the area caused discomfort for a large number of urban dwellers. Therefore, in this research, field measurements based on four environmental parameters (Ta, Tr, Va and RH) were conducted from 27 June 2023 to 7 July 2023 in three multi-courtyard traditional dwellings in the Tai Lake area to evaluate the ventilation performance and thermal comfort of the interior and semi-open spaces of the dwellings. The aim was to assess the role of semi-open space types and structures in the climate regulation of architectural spaces and their potential application in the design of modern dwellings to reduce summer discomfort. Semi-open spaces are effective in promoting natural ventilation to cool the building. This cooling effect is not due to the semi-open spaces themselves having lower temperatures. The indoor thermal environment was influenced by the outdoor climate and had a lagging effect. In addition, the ventilation performance of the semi-open space inside alley was the best, followed by the patio closest to the door.

Classification of Art Objects in the Context of Interior Space Design

The aim of the article is to establish the main categories for classifying art objects with the definition and study of their characteristics regarding the visual and functional impact on the design of interior space, taking into account both traditional and modern trends. Research methods include comparative analysis, field survey, description, systematization and generalization, as well as the results of many years of creative project practice. The scientific novelty lies in the proposed classification of art objects to create a coherent system in terms of its use in the design of interior space. The results of the research are based on the analysis of examples of modern art and project practice. Conclusions. In the process of research, a classification of art objects was created according to six basic categories, which allow tracking the peculiarities of the functioning of a certain art object in the interior. The first of the categories considered the distinction by types of art, according to which it was determined that in relation to traditional types of art, the art object functions, complementing the general artistic concept of the interior, establishing a figurative connection with its space; instead, correlated with modern forms of art, the art object acquires features and a way of functioning of non-traditional arts with modern means of expression, technologies and materials. The second category of division is by function: the predominance of the utilitarian function in an art object allows its introduction as a constructive element of the interior or equipment; while the predominance of the aesthetic function can state the decorative use of the art object. The third category of dividing art objects is by size: large-sized art objects are designed for perception in a sufficiently large space from a long distance; small-sized art objects are designed for perception from a close distance in smaller rooms. The fourth category is based on the form of expression: the realistic form is based on images that correspond to nature and gives the interior space a traditional character; instead, the abstract form with the use of non-realistic means of expression endows the interior space with features of modernity and uncertain content. The fifth category of division is by style: accordingly, the modern style of art objects involves involvement in various currents and directions of modern art, and the means of expression change the traditional appearance of space and its filling; instead, traditional stylistics uses classical forms and means of expression characteristic of known historical trends. The sixth category of division is based on materials: art objects with the use of traditional materials reveal the specificity and structure corresponding to nature, and in the visual perception of the interior space, they give it comprehensibility, basicity and reliability; instead, modern materials allow you to create new forms in the interior space with the help of art objects.

Politicising the Public Space: On Dalit Women Sanitation Workers in India

Caste determines the life worlds of people in India in particular and South Asia in general. Historically, it is observed that caste has conditioned the nature of public spaces. Upper castes can appropriate the public spaces legitimized by caste ideology and practice. However, colonial and post-colonial India witnessed changes in the caste system due to its (modern) legal interventions. Paradoxically, caste persists in its crude and subtle forms. It has also acquired new forms in post-independent public spaces. Caste determines certain bodily dispositions within the so-called public spaces. The ambiguous nature of modernity and the weight of tradition have drastically transformed the public space. A socially regulated economy and public institutions are determining the people, space, and mobility of the castes, too. This article investigates the nature of the stigmatized labour of Dalit women sanitation workers (who come under the manual scavenging community) within diverse public urban spaces. It analyses the various questions related to the Dalit women sanitation workers who work in select public universities, urban housing colonies, and slums in Delhi, India. It probes the Dalit women sanitation workers’ day-to-day life in caste-ridden spaces of urban- “public” spaces. One of the central questions that needs to be addressed is whether the socioeconomic space of these Dalit women workers has changed in contemporary India. Why do Dalit women have to do stigmatized work in public spaces? How are purity and pollution reinforced in elusive ways? Thus, it initiates a critique of the Indian feminist understanding of public spaces. This article acts as a way to engage with the epistemic priority of women sanitation workers to problematize Brahmanic feminism in India. Can there be any social-political engagement with the public space in the case of Dalit women sanitation workers? At the level of theory, this article critiques the dominant-Habermasian idea of the public sphere and Nancy Fraser’s counter-public to reflect on conceptual practice grounded in the Dalit women sanitation workers and public space.

On the behavior at infinity of complete spacelike hypersurfaces in a Lorentzian space form

On the behavior at infinity of complete spacelike hypersurfaces in a Lorentzian space form

On the inverse mean curvature flow by parallel hypersurfaces in space forms

We consider the inverse mean curvature flow by parallel hypersurfaces in space forms. We show that such a flow exists if and only if the initial hypersurface is isoparametric. The flow is characterized by an algebraic equation satisfied by the distance function of the parallel hypersurfaces. The solutions to the flow are obtained explicitly when the distinct principal curvatures have the same multiplicity. This is an additional assumption only for isoparametric hypersurfaces of the hyperbolic space or of the sphere with two or four distinct principal curvatures. The boundaries of the maximal interval of definition, when finite, are determined in terms of the number g g of distinct principal curvatures, their multiplicities m m and the mean curvature H H of the initial hypersurface. We describe the collapsing submanifolds of the flow at the boundaries of the interval. In particular, we show in the Euclidean space the solutions are eternal, while in the hyperbolic space there are eternal and immortal solutions. Starting with a connected isoparametric submanifold of the sphere, we show that the flow is an ancient solution, that collapses into a minimal hypersurface whose square length of its second fundamental form and its scalar curvature are constants given in terms of g g and n n . The minimal hypersurface is totally geodesic when g = 1 g=1 , it is a Clifford minimal hypersurface of the sphere when g = 2 g=2 and it is a Cartan type minimal submanifold when g ∈ { 3 , 4 , 6 } g\in \{3,4,6\} .

The Sociality of Form: Camillo Sitte's Urban Morphologies

AbstractThis article examines a text by a lesser‐known figure of fin‐de‐siècle Vienna, Camillo Sitte's Der Städtebau nach seinen künstlerischen Grundsätzen (1889), tracing the relationship between urban form and social structure in Sitte's treatise. It identifies the key points of this relationship in terms of causality: the form of public spaces can determine the form of social life; surrogacy: the throngs of the places’ inanimate inhabitants, the statues and monuments, are placeholders for the missing human gatherings; and finally displacement: the thick sociality of community life is transferred onto a heightened relationality with urban forms. Sitte's text sublimates the social; it diffuses abstract social structures—density, relationality, connection—onto the spatial morphologies of the city. Ultimately, this diffusion results in a capacious yet weakened model of sociality.

On a stratification of positive scalar curvature compact manifolds

For a compact PSC Riemannian [Formula: see text]-manifold [Formula: see text], the metric constant [Formula: see text] is defined to be the infinimum over [Formula: see text] of the spectral scalar curvature [Formula: see text] of [Formula: see text], where [Formula: see text] are the eigenvalues of the curvature operator of [Formula: see text] and [Formula: see text] is the maximal eigenvalue. The functional [Formula: see text] is continuous, re-scale invariant and defines a stratification of the space of PSC metrics over [Formula: see text]. We introduce as well the smooth constant [Formula: see text], which is the supremum of [Formula: see text] over the set of all PSC Riemannian metrics [Formula: see text] on [Formula: see text]. In this paper, we show that in the top layer, compact manifolds with [Formula: see text] are positive space forms. No manifolds have their [Formula: see text] in the interval [Formula: see text]. The manifold [Formula: see text] and arbitrary connected sums of copies of it with connected sums of positive space forms all have [Formula: see text]. For [Formula: see text], we prove that the manifolds [Formula: see text] take the intermediate values [Formula: see text]. From the bottom, we prove that simply connected (resp. [Formula: see text]-connected, [Formula: see text]-connected and non-string) compact manifolds of dimension [Formula: see text] (resp. [Formula: see text], [Formula: see text]) have [Formula: see text] (resp. [Formula: see text], [Formula: see text]). The proof of these last three results is based on surgery. In fact, we prove that the smooth [Formula: see text] constant doesn’t decrease after a surgery on the manifold with adequate codimension.

The quantization of Maxwell theory in the Cauchy radiation gauge: Hodge decomposition and Hadamard states

AbstractThe aim of this paper is to prove the existence of Hadamard states for the Maxwell equations on any globally hyperbolic spacetime. This will be achieved by introducing a new gauge fixing condition, the Cauchy radiation gauge, that will allow to suppress all the unphysical degrees of freedom. The key ingredient for achieving this gauge is a new Hodge decomposition for differential ‐forms in Sobolev spaces on complete (possibly noncompact) Riemannian manifolds.

Framed Bertrand and Mannheim Curves in Three-Dimensional Space Forms of Non-zero Constant Curvatures

The purpose of this paper is to generalize definitions of Bertrand and Mannheim curves to non-null framed curves and to non-flat three-dimensional (Riemannian or Lorentzian) space forms. Denote by $\mathbb{M}_q^n(c)$ the $n$-dimensional space form of index $q=0,1$ and constant curvature $c\neq 0$. We introduce two types of framed Bertrand curves and framed Mannheim curves in $\mathbb{M}_q^3(c)$ by using two different moving frames: the general moving frame and the Frenet-type frame. We investigate geometric properties of these framed Bertrand and framed Mannheim curves in $\mathbb{M}_q^3(c)$ that may have singularities. We then give characterizations for a non-null framed curve to be a framed Bertrand curve or to be a framed Mannheim curve. We show that in special cases these characterizations reduce to the well-known classical formulas: $\lambda \kappa+\mu \tau=1$ for Bertrand curves and $\lambda(\kappa^2+\tau^2)=\kappa$ for Mannheim curves. We provide several examples to support our results, and we visualize these examples by using the Hopf map, the hyperbolic Hopf map, and the spherical projection.

Homogeneous Riemannian Structures in Thurston Geometries and Contact Riemannian Geometries

We give explicit parametrizations for all the homogeneous Riemannian structures on model spaces of Thurston geometry. As an application, we give all the homogeneous contact metric structures on $3$-dimensional Sasakian space forms.

On Locally Conformal Kaehler Submersions

We study locally conformal Kaehler submersions, i.e., almost Hermitian submersions whose total manifolds are locally conformal Kaehler. We prove that the vertical distribution of a locally conformal Kaehler submersion is totally geodesic iff the Lee vector field of total manifold is vertical. We also obtain the O'Neill tensors $\tilde{\mathcal{A}}$ and $\tilde{\mathcal{T}}$ with respect to the Weyl connection of a locally conformal Kaehler submersion. Then, we proved that the horizontal distribution of such a submersion is integrable iff $\tilde{\mathcal{A}} \equiv 0$. Finally, we get Chen-Ricci inequalities for locally conformal Kaehler space form submersions and Hopf space form submersions.