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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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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
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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, Radu-Ioan Mihai
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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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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 $ $. 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
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Degenerate Hessian structures on radiant manifolds [PDF]
International Journal of Geometric Methods in Modern Physics, 2017 We present a rigorous mathematical treatment of Ruppeiner geometry, by considering degenerate Hessian metrics defined on radiant manifolds. A manifold $M$ is said to be radiant if it is endowed with a symmetric, flat connection $\bar\nabla$ and a global ...
García-Ariza, M. Á.
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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 $\mathbb{R}^{n^2}$.
Birtea, Petre, Comănescu, Dan
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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
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Curvature of Hessian manifolds [PDF]
Differential Geometry and its Applications, 2014 18 ...
S. Amari, J. Armstrong
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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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