Results 1 to 10 of about 2,645,036 (193)
A New Algebraic Inequality and Some Applications in Submanifold Theory
Mathematics, 2021 We give a simple proof of the Chen inequality involving the Chen invariant δ(k) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality.
Ion Mihai
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Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms [PDF]
Entropy, 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 ...
Bang-Yen Chen +2 more
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Explicit Geodesic Projection Distance on the Statistical Manifold of Multivariate Elliptical Distributions [PDF]
EntropyGeodesic projection distances on statistical manifolds have been widely applied across various research fields. Nevertheless, the existing closed-form solution is only available for the Gaussian manifold.
Xiangbing Chen +2 more
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Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds [PDF]
Mathematics, 2019 Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products R ×
Aliya Naaz Siddiqui +2 more
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Statistical cosymplectic manifolds and their submanifolds
پژوهشهای ریاضی, 2022 Introduction Let p(x,ζ) be the set of parametric probability distribution with parameter ζ=ζ1,…,ζn∊Rn. This set is called a statistical model or manifold. The distance between two points is measured by the Fisher metric. In general, statistical manifolds
Mohammad Bagher Kazemi, Shiva Salahvarzi
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Extremities for statistical submanifolds in Кenmotsu statistical manifolds
Filomat, 2021 Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples.
Siddiqui, Aliya Naaz +2 more
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On Nearly Sasakian and Nearly Kähler Statistical Manifolds
Mathematics, 2023 In this paper, we introduce the notions of nearly Sasakian and nearly Kähler statistical structures with a non-trivial example. The conditions for a real hypersurface in a nearly Kähler statistical manifold to admit a nearly Sasakian statistical ...
Siraj Uddin +3 more
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Mathematics, 2021 The Chen first inequality and a Chen inequality for the δ(2,2)-invariant on statistical submanifolds of Sasaki-like statistical manifolds, under a curvature condition, are obtained.
Hülya Aytimur +2 more
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Exponential arcs in manifolds of quantum states
Frontiers in Physics, 2023 The manifold under consideration consists of the faithful normal states on a sigma-finite von Neumann algebra in standard form. Tangent planes and approximate tangent planes are discussed. A relative entropy/divergence function is assumed to be given. It
Jan Naudts
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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
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