Results 11 to 20 of about 514 (177)
Hessian manifolds of nonpositive constant Hessian sectional curvature [PDF]
Tohoku Mathematical Journal, 2013 We classify the maximal Hessian manifolds of constant Hessaian sectional curvature nonpositive.
Hitoshi Furuhata, Takashi Kurose
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Locally conformally Hessian and statistical manifolds
Journal of Geometry and Physics, 2023 A statistical manifold $\left(M,D,g\right)$ is a manifold $M$ endowed with a torsion-free connection $D$ and a Riemannian metric $g$ such that the tensor $D g$ is totally symmetric. If $D$ is flat then $\left(M,g,D\right)$ is a Hessian manifold. A locally conformally Hessian (l.c.H) manifold is a quotient of a Hessian manifold $(C,\nabla,g)$ such that ...
Pavel Osipov
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Hessian Equations of Krylov Type on Kähler Manifolds
Journal of Geometric Analysis, 2023 In this paper, we consider Hessian equations with its structure as a combination of elementary symmetric functions on closed Kähler manifolds. We provide a sufficient and necessary condition for the solvability of these equations, which generalize the results of Hessian equations and Hessian quotient equations.
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Golden and Metallic Structures on Hessian Manifolds
MathematicsWe consider the reciprocal cost function J(x)=12(x+x−1)−1 and its n-dimensional extension J(x1,…,xn)=12(R+R−1)−1,R=∏i=1nxiαi,α=(α1,…,αn)∈Rn∖{0}. In logarithmic coordinates ti=logxi, the Hessian of J has a rank of one at every point.
Jonathan Washburn, Milan Zlatanović
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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
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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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On Hypersurfaces of Hessian Manifolds with Constant Hessian Sectional Curvature [PDF]
Journal of Mathematics and Statistics, 2005 In this study, we give one instrinsic inequality for Riemannian hypersurfaces in Hessian manifolds and sufficient and necessary condition for such hypersurfaces to be totally geodesic.
Mehmet Bektas +2 more
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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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The Pontryagin Forms of Hessian Manifolds [PDF]
, 2015 We show that Hessian manifolds of dimensions 4 and above must have vanishing Pontryagin forms. This gives a topological obstruction to the existence of Hessian metrics. We find an additional explicit curvature identity for Hessian 4-manifolds. By contrast, we show that all analytic Riemannian 2-manifolds are Hessian.
John Armstrong, Shun-ichi Amari
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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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