Space Form Research Articles

The lifts of surfaces in neutral 4-manifolds into the 2-Grassmann bundles

A twistor lift of a space-like or time-like surface in a neutral hyperKähler 4-manifold with zero mean curvature vector is given by a (para)holomorphic function, which yields (para)holomorphicity of the Gauss maps of space-like or time-like surfaces in E24 with zero mean curvature vector. For a space-like or time-like surface in an oriented neutral 4-manifold with zero mean curvature vector such that both twistor lifts belong to the kernel of the curvature tensor, its (para)complex quartic differential is holomorphic. If both twistor lifts of a time-like surface with zero mean curvature vector have light-like or zero covariant derivatives, then either the shape operator with respect to a light-like normal vector field vanishes or all the shape operators of the surface are light-like or zero. Examples with the former (resp. latter) property are given by the conformal Gauss maps of time-like surfaces of Willmore type with zero paraholomorphic quartic differential (resp. time-like surfaces in 4-dimensional neutral space forms based on the Gauss-Codazzi-Ricci equations).

Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle

We determine the general natural metrics G on the total space TM of the tangent bundle of a Riemannian manifold (M,g) such that the Schouten–van Kampen connection ∇¯ associated to the Levi-Civita connection of G is (quasi-)statistical. We prove that the base manifold must be a space form and in particular, when G is a natural diagonal metric, (M,g) must be locally flat. We prove that there exist one family of natural diagonal metrics and two families of proper general natural metrics such that (TM,∇¯,G) is a statistical manifold and one family of proper general natural metrics such that (TM∖{0},∇¯,G) is a quasi-statistical manifold.

Proactive health interventions in the workplace: The role of spatial playfulness in promoting mental health.

The high prevalence of mental illnesses has a serious impact on productive life and there is an urgent need to intervene using a variety of active and effective measures. The concept of playfulness in space is introduced into the design of work spaces oriented towards active health interventions, creating a close interaction between the body and the space through play, thus developing a positive effect on the promotion of the physical and mental health of the staff. With the help of the spatial order theory, the analysis of the interaction between body and space is attempted to explore the form, structure and scene of space in order to optimize the body's perception, cognition and behavior in the space, thus creating an indoor workspace model with positive intervention effects on human health. Based on the idea of spatial playful participation in active health interventions, this study explores the interaction between the body and the architectural space to enhance the perception and cognitive guidance of the space for the individual and to have a pleasant spiritual experience in the interaction to relieve work stress and enhance mental health. This series of discussions on the relationship between architectural space and the human body is of great relevance in improving the public health of occupational groups.

Spatiotemporal evolution and influencing factors of water resource green efficiency in the cities of the Yangtze River Economic Belt.

Effectively utilizing water resources, which is a fundamental natural resource and a vital economic resource, directly impacts how a country's economy develops. In this study, the Super-SBM model is used to calculate the city water resource green efficiency (CWRGE) of the Yangtze River Economic Belt (YREB), 108 cities that are prefecture level or higher, from 2006 to 2021. And its temporal and spatial evolution as well as its affecting variables are examined. The results indicate that, as a whole, the YREB's CWRGE has not yet achieved an effective level. The CWRGE in the YREB generally exhibits a trend of "first decreasing and then increasing, then decreasing and then increasing" and shows a "W"-shaped evolution law, and the overall trend is upward. There are just seven cities with effective data envelopment analysis (DEA), namely Changzhou, Hangzhou, Shanghai, Xuzhou, Changde, Changsha, and Yuxi. During the reporting period, the CWRGE of cities of various scales showed significant gaps: mega cities > big cities > small and medium-sized cities. From a regional perspective, the highest rate of CWRGE was found downstream of the YREB cities, then upstream, and the middle was the lowest. Spatial correlation findings demonstrated that both the agglomeration range and the outlier range were distributed, and there were mainly two positive aggregations of space forms ("high-high (H-H) type" and "low-low (L-L) type"), and the spatial distribution changed. The results of the spatiotemporal evolution demonstrate that there are more and more cities with high efficiency, as well as cities with low efficiency. From the results of the Tobit regression model, the CWRGE in the YREB are significantly improved by the economical development level, industrial scale, and water usage structure. While foreign direct investment and environmental regulation have considerable detrimental impacts, the impact of scientific and technological investment is not significant.

The hegemony of values: Revisiting Stanisław Pietraszko’s concept of culture with Antonio Gramsci’s theory of hegemony

In my reinterpretation of Stanisław Pietraszko’s writings, I seek to identify their elements that exhibit some affinity with the concept of cultural hegemony, which germinated from entirely different ideological soil and has been developed under different historical circumstances. The idea of hegemony is usually traced back to Antonio Gramsci’s texts, though also to the work of other scholars inspired by Karl Marx’s thought, including the British philosophers who founded cultural studies. I argue that in distancing himself from all Marxism-underpinned theories, therein those that evolved toward semiology, Pietraszko was prompted not only by his philosophical views on the ontology of culture and possibilities of studying it but also by the social and political conjuncture in which hedeveloped his conception of culture (specifically, the socialist or communist regimes in Eastern Europe). I ponder how the two divergent models of understanding culture (i.e. culture defined in terms of ways of life and the idea of cultural hegemony) can be brought together. In my argument, I consider various media and communication forms in public space, such as murals, graffiti, posters, billboards, monuments and the like. It is in them that I see manifestations of values.

Rigidity of weighted Einstein smooth metric measure spaces

We study the geometric structure of weighted Einstein smooth metric measure spaces with weighted harmonic Weyl tensor. A complete local classification is provided, showing that either the underlying manifold is Einstein, or decomposes as a warped product in a specific way. Moreover, if the manifold is complete, then it either is a weighted analogue of a space form, or it belongs to a particular family of Einstein warped products.

The Restorative Potential of Green Cultural Heritage: Exploring Cultural Ecosystem Services’ Impact on Stress Reduction and Attention Restoration

Green cultural heritage is an important form of natural space in cities. Only a few studies have conducted restorative studies in a historical environment as most have focused on natural environments. Moreover, few studies on cultural ecosystem services (CESs) have addressed cultural heritage. Based on an onsite questionnaire distributed to green cultural heritage users (N = 64) in Hamarikyu Garden, this paper explores the value of CESs in a green cultural heritage site and the relationship between cultural ecosystem values and perceived attention restoration/stress reduction. A multiple linear regression analysis and simple linear regression analyses were used to examine the data. The results showed that (1) the cultural ecosystem values of the green cultural heritage site were all rated highly except for the sense of place; (2) spending time in green cultural heritage provided respondents significant perceived attention restoration and stress reduction; (3) aesthetics and cultural heritage significantly affected perceived stress reduction, while attention restoration showed a significant positive correlation with aesthetic value and sense of place; and (4) the more visitors perceived the value of CESs, the more significant the perceived stress reduction and attention recovery were. This study indicates that CESs represent a useful tool for measuring the environmental characteristics of green cultural heritage sites and can predict perceived psychological recovery in green cultural heritage sites. Our findings enhance our knowledge about restorative environmental attributes through objective descriptions of potential health-promoting qualities and can be utilized as inspiration for designing restorative environments in green cultural heritage sites.

Art and Philosophy: Harmony of Giring-Giring Dance, Manganjan Dance, Tambun Bungai Dance of Kalimantan Tengah

The possibility of tradition collaborating with dance, music and performance art is an amazing art. However, it becomes problematic if the space to perform one of the parts of tradition, namely dance as an art or work in certain regions or localities, is still minimal. Either from the history of dances from certain regions, for example Central Kalimantan, especially the Ma'anyan Dayak community, or the method of usage or meaningful values in the form of ribut rukun, togetherness, care and exploration space. This research method uses a literature review that examines the results of previous studies as secondary sources, online media, and accompanying photos of dances originating from Central Kalimantan. The findings show that the Dayak Giring-Giring dance, Manganjan Dance and Tambun Bungai Dance have a variety of cultural richness, the meaning of friendship, as well as a rich history that must get space from generation to generation to the global community as a cultured, dignified, valuable and communal dance.

Semi-slant submanifolds in a locally conformal Kaehler space form

In this paper, we consider semi-slant submanifolds in a locally conformal Kaehler manifold and a locally conformal Kaehler space form. We give inequalities for the length of the second fundamental form and the mean curvature and, using Gauss and Codazzi equations, we get many useful results in locally conformal Kaehler space form.

Identification of polynomial nonlinear systems based on center manifold

A center-manifold (CM) based system identification (SID) method is developed to identify multi-input-multi-output continuous-time polynomial nonlinear systems in the state–space form. On one hand, the CM method is a natural extension of the frequency-domain subspace method to nonlinear SID problems. It decomposes the nonlinear SID problem into a series of linear least-square problems (in a precise sense), which can be solved analytically. This is in contrast to many existing methods that rely on iterative search of the global minimum. On the other hand, it is also a generalization of the invariant-subspace (ISP) based SID method. It inherits the nice property of the ISP method that the advantages of time-domain and frequency-domain SID methods are combined. In the paper, a persistence of excitation (PE) condition for the CM method is derived, which is described by the rank of certain Khatri–Rao product. Under the PE condition, the identification error is shown to be bounded within an arbitrarily small neighborhood of the origin when measurement noise is presented.

Desain Interior Perpustakaan Fakultas Bahasa Dan Seni Universitas Negeri Padang Dengan Konsep Minimalis

The low interest in reading has hampered intellectual abilities in society, especially students, so that libraries are required to be able to keep up with the pace of development of the times with services and infrastructure that meet the needs of space users, but the FBS UNP library has not been optimal in terms of interior design standards. Student complaints such as unstable air circulation, lack of reading space, and incomplete facilities have caused inconvenience, so an interior design of the FBS UNP Library was held with a minimalist concept. The purpose of interior design is to design a library layout that is representative and in accordance with interior design standards in order to create a sense of security and comfort for visitors while in the room. The interior design of the FBS UNP Library refers to the application of library interior design standards in the form of space, variety, hierarchy, lighting, personal areas, and comfort. The design method uses the 4D design method, namely Define (Defining) Design (Design), Develop (Development) and Dissaminate (Dissemination). Data collection is done by way of interviews, observation and documentation. Works are presented in the form of an Artwork Report with the main works being Presentation Mockups, Animation Videos and Presentation Posters.

The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$

We study the second fundamental form of the Siegel metric in $\mathcal A_5$ restricted to the locus of intermediate Jacobians of cubic threefolds. We prove that the image of this second fundamental form, which is known to be non-trivial, is contained in the kernel of a suitable multiplication map. Some ingredients are: the conic bundle structure of cubic threefolds, Prym theory, Gaussian maps and Jacobian ideals.

Concircular Hypersurfaces and Concircular Helices in Space Forms

In this paper, we find a full description of concircular hypersurfaces in space forms as a special family of ruled hypersurfaces. We also characterize concircular helices in 3-dimensional space forms by means of a differential equation involving the concircular factor and their curvature and torsion, and we show that the concircular helices are precisely the geodesics of the concircular surfaces.

A new geometric flow on 3-manifolds: the K-flow

We define a new geometric flow, which we shall call the K-flow, on 3-dimensional Riemannian manifolds; and study the behavior of Thurston’s model geometries under this flow both analytically and numerically. As an example, we show that an initially arbitrarily deformed homogeneous 3-sphere flows into a round 3-sphere and shrinks to a point in the unnormalized flow; or stays as a round 3-sphere in the volume normalized flow. The K-flow equation arises as the gradient flow of a specific purely quadratic action functional that has appeared as the quadratic part of New Massive Gravity in physics; and a decade earlier in the mathematics literature, as a new variational characterization of three-dimensional space forms. We show the short-time existence of the K-flow using a DeTurck-type argument.

Rellich inequalities via Riccati pairs on model space forms

We present a simple method for proving Rellich inequalities on Riemannian manifolds with constant, non-positive sectional curvature. The method is built upon simple convexity arguments, integration by parts, and the so-called Riccati pairs, which are based on the solvability of a Riccati-type ordinary differential inequality. These results can be viewed as the higher order counterparts of the recent work by Kajántó, Kristály, Peter, and Zhao, discussing Hardy inequalities using Riccati pairs.

Classification of semi-parallel hypersurfaces of the product of two spheres

It is known that Mendonça and Tojeiro (2013) [19] have established a complete classification of parallel submanifolds in the product manifold Qk1n1×Qk2n2, where Qk1n1 (resp. Qk2n2) is an n1-dimensional (resp. n2-dimensional) real space form with constant curvature k1 (resp. k2). In this paper, motivated by this result with considering further generalization, we study those semi-parallel hypersurfaces in case Qk1n1=Sk1n1 and Qk2n2=Sk2n2 with k1,k2>0. As the main result, we classify semi-parallel hypersurfaces of Sk1n1×Sk2n2 for n1,n2≥2.

A classification of triharmonic hypersurfaces in a pseudo-Riemannian space form

The purpose of this article is to investigate triharmonic hypersurfaces Mtn in a pseudo-Riemannian space form Nt1n+1(c). Assuming that the shape operator is diagonalizable, we show that every CMC triharmonic hypersurface either has constant scalar curvature or it is minimal if cε>0 and every CMC triharmonic hypersurface is minimal if cε<0, where ε is the inner product of the unit normal vector of Mtn. Furthermore, we prove that any CMC triharmonic hypersurface with diagonalizable shape operator in a pseudo-Euclidean space Et1n+1 is actually minimal provided that zero is a principal curvature of multiplicity at most one.

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

Homology of Warped Product Semi-Invariant Submanifolds of a Sasakian Space Form with Semisymmetric Metric Connection

This paper focuses on the investigation of semi-invariant warped product submanifolds of Sasakian space forms endowed with a semisymmetric metric connection. We delve into the study of these submanifolds and derive several fundamental results. Additionally, we explore the practical implications of our findings by applying them to the homology analysis of these submanifolds. Notably, we present a proof demonstrating the absence of stable currents for these submanifolds under a specific condition.

From cakravartin to bodhisattva: Buddhist models for globalization

AbstractThis article examines globalization in an Asian context through the lens of two Buddhist concepts: the cakravartin and the bodhisattva. A cakravartin is a ruler who fuses spiritual and political power in his global reign. This article argues that the cakravartin represents one model of Buddhist globalization where the spread of the religion coincides with the growing military dominion of a BuddhGist king. A bodhisattva, on the other hand, is an enlightened being who has chosen to be reborn out of compassion with the entire suffering world. A bodhisattva watches over a ‘Buddha field’, or spiritual realm. Each Buddha field has its own laws, culture, language, or even separate forms of time and space. The bodhisattva provides a new model for understanding cultural diversity in the absence of a unified political power: the Buddhist world is a transnational network where new identities are negotiated.