Curvature Properties Research Articles

Generalized B-curvature tensor within the framework of Lorentzian β-Kenmotsu manifold

The objective of this paper is to study some curvature properties of generalized [Formula: see text]-curvature tensor on Lorentzian [Formula: see text]-Kenmotsu manifold. Here first, we describe certain vanishing properties of generalized [Formula: see text]-curvature tensor on Lorentzian [Formula: see text]-Kenmotsu manifold and obtained several interesting results. Next, we formulate [Formula: see text] semi-symmetric condition on Lorentzian [Formula: see text]-Kenmotsu manifold. Again, we discussed the generalized [Formula: see text] pseudo-symmetric condition on Lorentzian [Formula: see text]-Kenmotsu manifold. We also characterized generalized [Formula: see text] [Formula: see text]-recurrent Lorentzian [Formula: see text]-Kenmotsu manifold. Further, we deal with Lorentzian [Formula: see text]-Kenmotsu manifold satisfying [Formula: see text] condition.

Curvature sensing lipid dynamics in a mitochondrial inner membrane model

Membrane curvature is essential for many cellular structures and processes, and factors such as leaflet asymmetry, lipid composition, and proteins all play important roles. Cardiolipin is the signature lipid of mitochondrial membranes and is essential for maintaining the highly curved shapes of the inner mitochondrial membrane (IMM) and the spatial arrangement of membrane proteins. In this study, we investigate the partitioning behavior of various lipids present in the IMM using coarse-grained molecular dynamics simulations. This study explores curved bilayer systems containing phosphatidylcholine (PC), phosphatidylethanolamine (PE), and cardiolipin (CDL) in binary and ternary component mixtures. Curvature properties such as mean and Gaussian curvatures, as well as the distribution of lipids into the various curved regions of the cristae models, are quantified. Overall, this work represents an advance beyond previous studies on lipid curvature sensing by simulating these systems in a geometry that has the morphological features and scales of curvature consistent with regions of the IMM. We find that CDL has a stronger preference for accumulating in regions of negative curvature than PE lipids, in agreement with previous results. Furthermore, we find lipid partitioning propensity is dominated by sensitivity to mean curvature, while there is a weaker correlation with Gaussian curvature.

On harmonic and asymptotically harmonic Finsler manifolds

In the present paper we introduce and investigate some types of harmonic Finsler manifolds and find out the interrelation between them. We give some characterizations of such spaces in terms of the Finsler mean curvature of geodesic spheres and the Finsler Laplacian of the distance function induced by the Finsler metric. We investigate some properties of the Finsler mean curvature of geodesic spheres of different radii. We prove that certain harmonic Finsler manifolds are of isotropic S-curvature and isotropic Ricci curvature. Moreover, we give some examples of non-Riemannian Finsler harmonic manifolds of constant flag curvature and constant S-curvature. Finally, we provide a technique to construct harmonic Finsler manifolds of Randers type.

Projective change between G.R.C. exponential metrics and Randers metrics

In this paper, we find the necessary and sufficient conditions under which two classes of (α, β)-metrics, i.e. generalized Randers change (G.R.C.) exponential metric F = α exp(β/α) + ϵβ and Randers metric F˜ = ˜α + β˜ are projectively related. Note that α and ˜α are Riemannian metrics, β and β˜ are 1-forms on a manifold M with dimension n > 2 and ϵ ̸= 0 is a constant. Furthermore, we study this projective relation when F has special curvature properties.

On curvature related geometric properties of Hayward black hole spacetime

This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level 2, 2-quasi Einstein, generalized quasi-Einstein and Roter type manifold. Also, it is shown that the nature of the HBH spacetime is pseudosymmetric and it obeys several types of pseudosymmetries, such as, pseudosymmetry due to concircular, conformal and conharmonic curvature (i.e., F⋅F=LQ(g,F) for F=W,C,K with a smooth scalar function L), and it also possesses the relation R⋅R−LQ(g,C)=Q(S,R). It is engrossing to mention that the nature of energy momentum tensor of the HBH spacetime is pseudosymmetric. On the basis of curvature related properties, we have made a comparison among Reissner–Nordström spacetime, interior black hole spacetime and HBH spacetime. It is noteworthy to mention that the gravitational force of the point-like global monopole spacetime is much stronger than that of HBH spacetime. Also, it is shown that the HBH spacetime admits an almost η-Ricci soliton as well as an almost η-Ricci-Yamabe soliton. Finally, an elegant comparative study is delineated between the HBH spacetime and the point-like global monopole spacetime with respect to different kinds of symmetry, such as, motion, curvature collineation, curvature inheritance etc.

A machine learning framework for the identification of crops and weeds based on shape curvature and texture properties

A machine learning framework for the identification of crops and weeds based on shape curvature and texture properties

A Study on the Lateral Ultimate Strength and Collapse Modes of Doubly Curved Stiffened Plates

Bows and stems are often subjected to wave slamming loads. Stiffened plates with curvatures in both longitudinal and transversal directions are the basic members of these structures. As a result, it is important to investigate the lateral ultimate strength of the doubly curved stiffened plates. In this study, the non-linear finite element method (NFEM) is selected to investigate the collapse modes and lateral ultimate strengths of the doubly curved stiffened plates. Additionally, the influences of curvature and geometrical properties on the collapse modes and ultimate strengths of doubly curved stiffened plates are investigated. In the NFEM analysis, a series of numerical simulations, covering different aspect ratios, curvatures, and structural scantlings are performed. Different collapse modes of doubly curved stiffened plates under lateral loading cases are observed. The relationships between the collapse modes and the geometrical properties are then discussed based on the numerical results. Moreover, the results also show that larger curvatures along the stiffeners and stronger stiffeners contribute more to the lateral ultimate strengths. Subsequently, an empirical formula is derived and verified for predicting the lateral ultimate strength of the doubly curved stiffened plates. The results of the empirical formula match well with numerical calculations.

Three-Dimensional Semi-Symmetric Almost α-Cosymplectic Manifolds

The main objective of this paper is to study semi-symmetric almost α-cosymplectic three-manifolds. We present basic formulas for almost α-cosymplectic manifolds. Using curvature properties, we obtain some necessary and sufficient conditions on semi-symmetric almost α-cosymplectic three-manifolds. We obtain the main results under an additional condition. The paper concludes with two illustrative examples.

A topologically charged four-dimensional wormhole and the energy conditions

In this research work, our primary focus revolves around the examination of a specific category of traversable wormholes known as topologically charged generalized Schwarzschild-Simpson-Visser-type wormhole, ds 2 = -(1-(2M/√(x 2+b 2))) dt 2+(1-(2M/√(x 2+b 2)))-1 ·(dx 2/α2)+(x 2+a 2) (dθ 2+sin2 θ dϕ 2). This wormhole is uniquely defined by a pair of key parameters including global monopole charge. A noteworthy outcome of our investigation is the observation that the energy-momentum tensor associated with this wormhole complies with both the weak energy condition (WEC) and the null energy condition (NEC). Furthermore, incorporation of global monopole charge introduces a substantial influence on the curvature properties of wormhole space-time and various associated physical quantities derived from this geometry.

A study on the tangent bundle with the vertical generalized Berger type deformed Sasaki metric

In this paper, we introduce a vertical generalized Berger type deformed Sasaki metric on the tangent bundle $TM$ over an anti-paraK\"{a}hler manifold as a new natural metric. Firstly, we investigate the Levi-Civita connection of this metric and then we calculate all forms of the Riemannian curvature tensors. Also, we present some results concerning curvature properties. Finally, we study the geometry of $\varphi $-unit tangent bundle equipped with the vertical generalized Berger type deformed Sasaki metric.

A unified approach of detecting phase transition in time-varying complex networks

Deciphering the non-trivial interactions and mechanisms driving the evolution of time-varying complex networks (TVCNs) plays a crucial role in designing optimal control strategies for such networks or enhancing their causal predictive capabilities. In this paper, we advance the science of TVCNs by providing a mathematical framework through which we can gauge how local changes within a complex weighted network affect its global properties. More precisely, we focus on unraveling unknown geometric properties of a network and determine its implications on detecting phase transitions within the dynamics of a TVCN. In this vein, we aim at elaborating a novel and unified approach that can be used to depict the relationship between local interactions in a complex network and its global kinetics. We propose a geometric-inspired framework to characterize the network’s state and detect a phase transition between different states, to infer the TVCN’s dynamics. A phase of a TVCN is determined by its Forman–Ricci curvature property. Numerical experiments show the usefulness of the proposed curvature formalism to detect the transition between phases within artificially generated networks. Furthermore, we demonstrate the effectiveness of the proposed framework in identifying the phase transition phenomena governing the training and learning processes of artificial neural networks. Moreover, we exploit this approach to investigate the phase transition phenomena in cellular re-programming by interpreting the dynamics of Hi-C matrices as TVCNs and observing singularity trends in the curvature network entropy. Finally, we demonstrate that this curvature formalism can detect a political change. Specifically, our framework can be applied to the US Senate data to detect a political change in the United States of America after the 1994 election, as discussed by political scientists.

Some curvature properties of perfect fluid spacetimes

In this paper we assume that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and innovative approach, we investigate some curvature properties of perfect fluid spacetimes. Firstly, we provide a necessary condition for a Lorentzian manifold to be a perfect fluid spacetime. We prove that a conformally flat perfect fluid space-time is a spacetime of quasi constant sectional curvature. Also, we acquire that a conharmonically flat perfect fluid spacetime represents the radiation era. Next, we show that if a stiff matter fluid obeys Yang’s equations, then the vorticity of the fluid vanishes. Moreover, we find that if the Ricci tensor is Killing, then the perfect fluid spacetime is (i) expansion-free and shear-free, and its flow is geodesic, however, not necessarily vorticity-free, and (ii) σ and p are constant. Besides, we establish that Ricci semi-symmetric or Ricci symmetric perfect fluid spacetimes represent either dark matter era, or phantom era. Finally, we acquire that if a perfect fluid is Ricci symmetric, then either the spacetime represents a dark matter era, or a static spacetime.

Effect of Wheel Path in Raster Grinding on Surface Accuracy of an Off-Axis Parabolic Mirror

Off-axis parabolic mirrors have extensive applications in X-ray optics, with the precision of their curvature directly impacting grazing-incidence focusing performance. Notably, the off-axis parabolic surface has non-rotating and non-symmetrical characteristics. Ultra-precision raster grinding utilizing a diamond wheel is a common method. Crucially, establishing an optimal wheel path stands as the key to ensuring surface accuracy during off-axis paraboloid grinding. In this study, according to the double curvature property of an off-axis parabolic surface, two different wheel paths were compared: one tracing the meridian direction (parabolic generatrix) and the other following the arc vector direction (arc). The results showed that the wheel path in raster grinding stepping along the arc vector direction can obtain a smaller scallop height and higher surface accuracy. The surface accuracy of one step along the arc vector direction is 9.6 μm, and that of the other step along the meridian direction is 32.6 μm. A model of the scallop height was established based on the relative relationship between adjacent wheel paths, and the error is within 5%. According to the correlation between scallop height and shape error, we conducted an analysis of the spatial distribution of shape errors under varying wheel paths. The wheel path that steps along the arc vector is more suitable for raster grinding of the off-axis paraboloid. The above study can provide theoretical guidance for the wheel path planning of off-axis parabolic mirrors with high surface accuracy.

Transverse momentum and multiplicity dependence of varLambda _{c}^{+}/D^{0} ratio in pp collisions at sqrt{s}=13 TeV

We apply an equal-velocity quark combination model to study the varLambda _{c}^{+}/D^{0} ratio in the range p_{T}lesssim 10 GeV/c in pp collisions at sqrt{s}=13 TeV. We decompose the ratio into four parts which are related to quark numbers, light-flavor quark p_{T} spectrum, charm quark p_{T} spectrum, momentum correlation between light and charm quarks, respectively. Their influence on varLambda _{c}^{+}/D^{0} ratio is individually studied. The curvature property of light-flavor quark p_{T} spectrum is the main reason of the non-monotonic p_{T} dependence of varLambda _{c}^{+}/D^{0} ratio exhibited in high multiplicity events. Moreover, the multiplicity dependence of varLambda _{c}^{+}/D^{0} ratio as the function of p_{T} is mainly because of the multiplicity dependence of light-flavor quark p_{T} spectrum. Using the light-flavor quark p_{T} spectrum obtained from experimental data of light-flavor hadrons and charm quark p_{T} spectrum obtained from FONLL and/or PYTHIA calculations, the p_{T} dependence of experimental data of varLambda _{c}^{+}/D^{0} ratio in high multiplicity events and that in low multiplicity events in pp collisions at sqrt{s}=13 TeV are reasonably understood.

Curvature properties of spacelike hypersurfaces in a RW spacetime

Curvature invariants of both intrinsic and extrinsic nature play a significant role in elucidating the geometry of a spacetime. In particular, these invariants are useful in detecting event horizon of black holes. Notable examples of spacetimes are provided by the generalized Robertson-Walker (GRW) models. An (m+1)-dimensional GRW spacetime is a Lorentzian warped product I×fN endowed with the warped metric gˆ=−dt2+f2(t)g, having as base an open real interval I equipped with the metric −dt2 and as fiber any Riemannian space (N,g) of dimension m, where f is a smooth positive-valued function on I. In this article, we focus our study on the GRW spacetimes having the fiber a Riemannian space with metric g=gk of constant sectional curvature k and denoted by L1m+1(k,f), i.e. RW spacetimes. Using an approach originally developed in Decu et al. (2008) [46], we obtain in this work the lower bound of the (generalized) normalized Casorati curvatures for a spacelike hypersurface H in the GRW spacetime L1m+1(k,f) in terms of the (normalized) scalar curvature of H, the constant sectional curvature k of the fiber, the normal hyperbolic angle of the hypersurface and the warping function f. We also derive the conditions under which this lower bound is reached. We finally apply the results to some basic cosmological models, namely Lorentz-Minkowski, de Sitter, Einstein-de Sitter, anti de Sitter and steady state spacetimes.

The mid-level vision toolbox for computing structural properties of real-world images

Mid-level vision is the intermediate visual processing stage for generating representations of shapes and partial geometries of objects. Our mechanistic understanding of these operations is limited, in part, by a lack of computational tools for analyzing image properties at these levels of representation. We introduce the Mid-Level Vision (MLV) Toolbox, an open-source software that automatically processes low- and mid-level contour features and perceptual grouping cues from real-world images. The MLV toolbox takes vectorized line drawings of scenes as input and extracts structural contour properties. We also include tools for contour detection and tracing for the automatic generation of vectorized line drawings from photographs. Various statistical properties of the contours are computed: the distributions of orientations, contour curvature, and contour lengths, as well as counts and types of contour junctions. The toolbox includes an efficient algorithm for computing the medial axis transform of contour drawings and photographs. Based on the medial axis transform, we compute several scores for local mirror symmetry, local parallelism, and local contour separation. All properties are summarized in histograms that can serve as input into statistical models to relate image properties to human behavioral measures, such as esthetic pleasure, memorability, affective processing, and scene categorization. In addition to measuring contour properties, we include functions for manipulating drawings by separating contours according to their statistical properties, randomly shifting contours, or rotating drawings behind a circular aperture. Finally, the MLV Toolbox offers visualization functions for contour orientations, lengths, curvature, junctions, and medial axis properties on computer-generated and artist-generated line drawings. We include artist-generated vectorized drawings of the Toronto Scenes image set, the International Affective Picture System, and the Snodgrass and Vanderwart object images, as well as automatically traced vectorized drawings of set architectural scenes and the Open Affective Standardized Image Set (OASIS).

Yang-Mills Casimir wormholes in D = 2 + 1

This work presents new three-dimensional traversable wormhole solutions sourced by the Casimir density and pressures related to the quantum vacuum fluctuations in Yang-Mills (Y-M) theory. We begin by analyzing the noninteracting Y-M Casimir wormholes, initially considering an arbitrary state parameter ω and determine a simple constant wormhole shape function. Next, we introduce a new methodology for deforming the state parameter to find well-behaved redshift functions. The wormhole can be interpreted as a legitimate Casimir wormhole with an expected average state parameter of ω = 2. Then, we investigate the wormhole curvature properties, energy conditions, and stability. Furthermore, we discover a novel family of traversable wormhole solutions sourced by the quantum vacuum fluctuations of interacting Yang-Mills fields with a more complex shape function. Deforming the effective state parameter similarly, we obtain well-behaved redshift functions and traversable wormhole solutions. Finally, we examine the energy conditions and stability of solutions in the interacting scenario and compare to the noninteracting case.

Finsler Warped Product Metrics with Special Curvature Properties

The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space–time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we find differential equations of Finsler warped product metrics with vanishing χ-curvature or vanishing H-curvature. Furthermore, we show that, for Finsler warped product metrics, the χ-curvature vanishes if and only if the H-curvature vanishes.

Some extrinsic geometric characterizations of quasi-product production functions in microeconomics

The theory of production functions plays an important role in the field of economic analysis. The purpose of the current work is to investigate quasi-product production functions in microeconomics from the view of extrinsic invariants. Focussing on the geometric invariants of the corresponding quasi-product production surfaces, by solving some certain interesting differential equations we classify two-inputs quasi-product production functions whose production surfaces admit constant mean curvature property. Furthermore, a series of classification results and some interesting examples of quasi-product production functions are obtained, which could be applied to the study of economic analysis.

On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space

The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived an expression of Ricci curvature for the homogeneous generalized Matsumoto change. Moreover, we have deduced the expression of Ricci curvature for the aforementioned space with vanishing the S-curvature. These findings contribute significantly to understanding the complex nature of Finsler spaces and their curvature properties.