Hessian manifolds of nonpositive constant hessian sectional curvature
Hitoshi Furuhata,Takashi Kurose +1 more
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In this article, the maximal Hessian manifolds of constant Hessaian sectional curvature are classified as non-positive and maximal Hessians of Hessaians are considered.Abstract:
We classify the maximal Hessian manifolds of constant Hessaian sectional curvature nonpositive.read more
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Book
The geometry of Hessian structures
TL;DR: In this paper, a Riemannian metric g on a flat manifold M with flat connection D is called a Hessian metric if it is locally expressed by the Hessian of local functions ϕ with respect to the affine coordinate systems.
Hypersurfaces in Statistical Manifolds
TL;DR: The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given in this article as a first step of the statistical submanifold theory.
Book ChapterDOI
Geometry of Hessian Structures
TL;DR: A Riemannian metric g on a flat manifold M with flat connection D is called a Hessian metric if it is locally expressed by the Hessian of local functions ϕ with respect to the affine coordinate systems.
Journal ArticleDOI
Statistical submanifolds from a viewpoint of the Euler inequality
Naoto Satoh,Hitoshi Furuhata,Izumi Hasegawa,Toshiyuki Nakane,Yukihiko Okuyama,Kimitake Sato,Mohammad Shahid,Aliya Naaz Siddiqui +7 more
TL;DR: In this article, the Euler inequality for statistical submanifolds is generalized to include doubly autoparallel statistical submansifolds in warped product spaces, for which the equality holds at each point.
Journal ArticleDOI
Hessian Geometry on Lagrange Spaces
TL;DR: The correspondence between Hessian and Kahler metrics and curvatures to Lagrange spaces is extended and the results obtained are compared to those obtained in the previous chapter.
References
More filters
Book
The geometry of Hessian structures
TL;DR: In this paper, a Riemannian metric g on a flat manifold M with flat connection D is called a Hessian metric if it is locally expressed by the Hessian of local functions ϕ with respect to the affine coordinate systems.
Hypersurfaces in Statistical Manifolds
TL;DR: The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given in this article as a first step of the statistical submanifold theory.
Journal ArticleDOI
Hypersurfaces in statistical manifolds
TL;DR: In this paper, the condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given as a first step of the statistical submanifold theory.
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