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

Journal of inequalities and applications

Vladimir Slesar¹ 

关键词: scalar curvature;    mean curvature;    Casorati curvature;    shape operator;    quaternionic space form;    slant submanifold;    optimal inequality;   

DOI  :  10.1186/1029-242X-2014-123

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY