Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms-Reference-Cited by-同舟云学术

Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms

Published:2014-03-27 Issue:1 Volume:2014 Page:
ISSN:1029-242X
Container-title:Journal of Inequalities and Applications
language:en
Short-container-title:J Inequal Appl

Author:

Slesar Vladimir,Şahin Bayram,Vîlcu Gabriel-Eduard

Abstract

Abstract In this paper we prove two sharp inequalities that relate the normalized scalar curvature with the Casorati curvature for a slant submanifold in a quaternionic space form. Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Link

https://link.springer.com/content/pdf/10.1186/1029-242X-2014-123.pdf

Reference41 articles.

1. Chen B-Y: Some pinching and classification theorems for minimal submanifolds. Arch. Math. 1993, 60: 568-578.

2. Chen B-Y: δ -Invariants, inequalities of submanifolds and their applications. In Topics in Differential Geometry. Ed. Acad. Române, Bucharest; 2008:29-155.

3. Deng S: Improved Chen-Ricci inequality for Lagrangian submanifolds in quaternion space forms. Int. Electron. J. Geom. 2012,5(1):163-170.

4. Hong Y, Houh CS: Lagrangian submanifolds of quaternion Kaehlerian manifolds satisfying Chen’s equality. Beitr. Algebra Geom. 1998,39(2):413-421.

5. Liu X: On Ricci curvature of totally real submanifolds in a quaternion projective space. Arch. Math. 2002,38(4):297-305.

Cited by 25 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On $$\delta $$-Casorati curvature invariants of Lagrangian submanifolds in quaternionic Kähler manifolds of constant q-sectional curvature;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2023-04-24

2. Strongly minimal complex lightlike hypersurfaces;Hacettepe Journal of Mathematics and Statistics;2022-12-31

3. Inequalities for Riemannian Submersions Involving Casorati Curvatures: A New Approach;6th International Students Science Congress Proceedings Book;2022-09-10

4. Slant Submanifolds of Quaternion Kaehler and HyperKaehler Manifolds;Complex Geometry of Slant Submanifolds;2022

5. Curvature Inequalities for Slant Submanifolds in Pointwise Kenmotsu Space Forms;Contact Geometry of Slant Submanifolds;2022