Results 1 to 10 of about 514 (177)
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
doaj +5 more sources
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, Mihai Ion
exaly +4 more sources
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
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
doaj +2 more sources
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 +2 more
exaly +3 more sources
Hessian Operators on Constraint Manifolds [PDF]
Journal of Nonlinear Science, 2015 On a constraint manifold we give an explicit formula for the Hessian matrix of a cost function that involves the Hessian matrix of a prolonged function and the Hessian matrices of the constraint functions. We give an explicit formula for the case of the orthogonal group ${\bf O}(n)$ by using only Euclidean coordinates on $\mathbb{R}^{n^2}$.
Dan Comanescu, Petre Birtea
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.
Yawei Chu
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
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