Results 11 to 20 of about 17,583 (186)
Differential Geometry and its Applications, 1997 An affine manifold is Hessian if it possesses a Hessian metric, that is, a Riemannian metric which is locally the Hessian of a function. Hessian manifolds are the analogue of Kähler manifolds among affine manifolds and enjoy many strong properties. For example, the first theorem in the paper is that a simply connected affine manifold with a complete ...
Shima, Hirohiko, Yagi, Katsumi
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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
The Journal of Geometric Analysis, 2023 In this paper, we consider Hessian equations with its structure as a combination of elementary symmetric functions on closed K hler 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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Contravariant pseudo-Hessian manifolds and their associated Poisson structures [PDF]
Differential Geometry and its Applications, 2020 A contravariant pseudo-Hessian manifold is a manifold $M$ endowed with a pair $(\nabla,h)$ where $\nabla$ is a flat connection and $h$ is a symmetric bivector field satisfying a contravariant Codazzi equation. When $h$ is invertible we recover the known notion of pseudo-Hessian manifold. Contravariant pseudo-Hessian manifolds have properties similar to
Abdelhak Abouqateb +2 more
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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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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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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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Complex Manifolds, 2022 Let (M, ∇, 〈, 〉) be a manifold endowed with a flat torsionless connection r and a Riemannian metric 〈, 〉 and (TkM)k≥1 the sequence of tangent bundles given by TkM = T(Tk−1M) and T1M = TM. We show that, for any k ≥ 1, TkM carries a Hermitian structure (Jk,
Boucetta Mohamed
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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.
Furuhata, Hitoshi, Kurose, Takashi
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