A new proof for some optimal inequalities involving generalized normalized δ -Casorati curvatures

Journal of inequalities and applications

Chul Woo Lee¹ 

关键词: scalar curvature;    mean curvature;    δ-Casorati curvature;    shape operator;    quaternionic space form;    slant submanifold;    optimal inequality;    53A07;    49K35;   

DOI  :  10.1186/s13660-015-0831-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we give a new proof for two sharp inequalities involving generalized normalized δ-Casorati curvatures of a slant submanifold in a quaternionic space form. These inequalities were recently obtained in Lee and Vîlcu (Taiwan. J. Math. 19(3):691-702, 2015) using an optimization procedure by showing that a quadratic polynomial in the components of the second fundamental form is parabolic. The new proof is obtained analyzing a suitable constrained extremum problem on submanifold.

【 授权许可】

CC BY