Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

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.

Bibliographic Details
Main Authors: Adela Mihai, Ion Mihai
Format: Article
Language:English
Published: MDPI AG 2018-03-01
Series:Mathematics
Subjects:
statistical manifolds
Hessian manifolds
Hessian sectional curvature
scalar curvature
Ricci curvature
Online Access:http://www.mdpi.com/2227-7390/6/3/44
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spelling doaj-c130f85f44434a699c09b5699ff5496f2020-11-24T22:10:10ZengMDPI AGMathematics2227-73902018-03-01634410.3390/math6030044math6030044Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian CurvatureAdela Mihai0Ion Mihai1Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, RomaniaDepartment of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, RomaniaWe 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.http://www.mdpi.com/2227-7390/6/3/44statistical manifoldsHessian manifoldsHessian sectional curvaturescalar curvatureRicci curvature
collection DOAJ
language English
format Article
sources DOAJ
author Adela Mihai
Ion Mihai
spellingShingle Adela Mihai
Ion Mihai
Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature
Mathematics
statistical manifolds
Hessian manifolds
Hessian sectional curvature
scalar curvature
Ricci curvature
author_facet Adela Mihai
Ion Mihai
author_sort Adela Mihai
title Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature
title_short Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature
title_full Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature
title_fullStr Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature
title_full_unstemmed Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature
title_sort curvature invariants for statistical submanifolds of hessian manifolds of constant hessian curvature
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2018-03-01
description 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.
topic statistical manifolds
Hessian manifolds
Hessian sectional curvature
scalar curvature
Ricci curvature
url http://www.mdpi.com/2227-7390/6/3/44
work_keys_str_mv AT adelamihai curvatureinvariantsforstatisticalsubmanifoldsofhessianmanifoldsofconstanthessiancurvature
AT ionmihai curvatureinvariantsforstatisticalsubmanifoldsofhessianmanifoldsofconstanthessiancurvature
_version_ 1725808846909210624

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