Results 1 to 10 of about 458 (133)
The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature [PDF]
Entropy, 2020 We establish Chen inequality for the invariant δ ( 2 , 2 ) on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds.
Adela Mihai, Ion Mihai
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Mathematics, 2022 Chen’s first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature was obtained by B.-Y. Chen et al. Other particular cases of Chen inequalities in a statistical setting were given by different authors.
Ion Mihai, Mihai Ion
exaly +3 more sources
Gradient Systems and Asymmetric Relaxations in View of Riemannian Geometry [PDF]
EntropyIn dually flat manifolds, there is a deep connection between gradient flows and pregeodesics. This was one of the many important contributions of Amari to information geometry. In this paper, we extend the study of this relationship to general Riemannian
Alessandro Bravetti +2 more
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Mathematics, 2022 The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in ...
Aliya Naaz Siddiqui +2 more
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Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature
Mathematics, 2018 We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.
Adela Mihai, Ion Mihai, Mihai Adela
exaly +3 more sources
Hessian equations of Krylov type on compact Hermitian manifolds
Open Mathematics, 2022 In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix.
Zhou Jundong, Chu Yawei
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Cancer Reports, EarlyView., 2023 Abstract Background A methodology to assess the immune microenvironment (IME) of non‐small cell lung cancer (NSCLC) has not been established, and the prognostic impact of IME factors is not yet clear. Aims This study aimed to assess the IME factors and evaluate their prognostic values. Methods and Results We assessed CD8+ tumor‐infiltrating lymphocyte (
Yukihiro Terada +16 more
wiley +1 more source
On a class of obstacle problem for Hessian equations on Riemannian manifolds
Journal of Inequalities and Applications, 2023 In this paper, we establish the a priori C 2 $C^{2}$ estimates for solutions of a class of obstacle problem for Hessian equations on Riemannian manifolds. Some applications are also discussed. The main contribution of this paper is the boundary estimates
Jinxuan Liu, Yong Wang
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λ-Deformation: A Canonical Framework for Statistical Manifolds of Constant Curvature
Entropy, 2022 This paper systematically presents the λ-deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry.
Jun Zhang, Ting-Kam Leonard Wong
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Regularity of degenerate k-Hessian equations on closed Hermitian manifolds
Advanced Nonlinear Studies, 2022 In this article, we are concerned with the existence of weak C1,1{C}^{1,1} solution of the kk-Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation.
Zhang Dekai
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