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.
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2227-7390/6/3/44 |
| _version_ | 1811317471611715584 |
|---|---|
| author | Adela Mihai Ion Mihai |
| author_facet | Adela Mihai Ion Mihai |
| author_sort | Adela Mihai |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-13T12:08:36Z |
| format | Article |
| id | doaj.art-c130f85f44434a699c09b5699ff5496f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-13T12:08:36Z |
| publishDate | 2018-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c130f85f44434a699c09b5699ff5496f2022-12-22T02:47:34ZengMDPI 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 |
| 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 |
| title | 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_short | 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 |
| 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 |