Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection. [PDF]
Entropy (Basel), 2022 In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional ...
Decu S, Vîlcu GE.
europepmc +4 more sources
Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms. [PDF]
Entropy (Basel), 2021 The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manifolds of the ...
Chen BY, Decu S, Vîlcu GE.
europepmc +5 more sources
Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures [PDF]
Mathematics, 2018 A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections ∇ and ∇ * in the Sasakian statistical structure, we provide the ...
Chul Woo Lee, Jae Won Lee
doaj +5 more sources
Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature [PDF]
Mathematics, 2020 In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant ...
Simona Decu +2 more
doaj +5 more sources
Systematic Classification of Curvature and Feature Descriptor of 3D Shape and Its Application to "Complexity" Quantification Methods. [PDF]
Entropy (Basel), 2023 Generative design is a system that automates part of the design process, but it cannot evaluate psychological issues related to shapes, such as “beauty” and “liking”. Designers therefore evaluate and choose the generated shapes based on their experience.
Matsuyama K, Shimizu T, Kato T.
europepmc +2 more sources
Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms. [PDF]
Entropy (Basel), 2018 In this paper, we obtain the upper bounds for the normalized δ -Casorati curvatures and generalized normalized δ -Casorati curvatures for statistical submanifolds in Sasaki-like statistical manifolds with constant curvature. Further,
Alkhaldi AH +3 more
europepmc +2 more sources
Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature. [PDF]
Entropy (Basel), 2018 In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati
Decu S +3 more
europepmc +2 more sources
On the Extrinsic Principal Directions and Curvatures of Lagrangian Submanifolds
Mathematics, 2020 From the basic geometry of submanifolds will be recalled what are the extrinsic principal tangential directions, (first studied by Camille Jordan in the 18seventies), and what are the principal first normal directions, (first studied by Kostadin ...
Marilena Moruz, Leopold Verstraelen
doaj +3 more sources
A new proof for some optimal inequalities involving generalized normalized δ-Casorati curvatures [PDF]
Journal of Inequalities and Applications, 2015 Let \(M\) be an \(n\)-dimensional Riemannian submanifold of a Riemannian manifold \((\bar{M},\bar{g})\). Then it is known that the Casorati curvature of \(M\) is an extrinsic invariant defined as the normalized square of the length of the second fundamental form \(h\) of the submanifold (of dimension \(n\)).
Chul Woo Lee +2 more
core +5 more sources
Iperception, 2015 Local solid shape applies to the surface curvature of small surface patches—essentially regions of approximately constant curvatures—of volumetric objects that are smooth volumetric regions in Euclidean 3-space.
Koenderink J, van Doorn A, Wagemans J.
europepmc +2 more sources