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Selfsimilar Hessian manifolds [PDF]

Journal of Geometry and Physics, 2022
A selfsimiar manifold is a Riemannian manifold $\left(M,g\right)$ endowed with a homothetic vector field $ξ$. We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian manifold or a Eucledean space.
Pavel Osipov
exaly   +4 more sources

Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

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 ...
Lamia Saeed Alqahtani, Ali Alkhaldi, Aliy Naaz Siddiqui   +2 more
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Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature [PDF]

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
doaj   +2 more sources

Geometry of Hessian manifolds

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 ...
Hirohiko Shima
exaly   +2 more sources

Complex Hessian Equations on Some Compact Kähler Manifolds [PDF]

International Journal of Mathematics and Mathematical Sciences, 2012
On a compact connected 2m-dimensional Kähler manifold with Kähler form ω, given a smooth function f:M→ℝ and an integer ...
Asma Jbilou
doaj   +4 more sources

Complex Hessian Equation on Kähler Manifold [PDF]

International Mathematics Research Notices, 2009
12 ...
exaly   +3 more sources

Generalized Legendre Transforms Have Roots in Information Geometry [PDF]

Entropy
Artstein-Avidan and Milman [Annals of mathematics (2009), (169):661–674] characterized invertible reverse-ordering transforms in the space of lower, semi-continuous, extended, real-valued convex functions as affine deformations of the ordinary Legendre ...
Frank Nielsen
doaj   +2 more sources

An Approach to Fisher-Rao Metric for Infinite Dimensional Non-Parametric Information Geometry [PDF]

Entropy
Non-parametric information geometry has long faced an “intractability barrier”: in the infinite-dimensional setting, the Fisher–Rao metric is a weak Riemannian metric functional that lacks a bounded inverse, rendering classical optimization and ...
Bing Cheng, Howell Tong
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Relative-Entropy Variational Principle for Semiclassical Gravity with Finite-Resolution Boundaries [PDF]

Entropy
This work formulates semiclassical gravity within a causal-diamond framework where a finite-resolution boundary provides the edge structure for a local Wheeler–DeWitt description.
Olivier Nusbaumer
doaj   +2 more sources

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
exaly   +4 more sources