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

被引：11

作者：

Lee, Chul Woo ^{[1
]}

Lee, Jae Won ^{[2
]}

Vilcu, Gabriel-Eduard ^{[3
,4
]}

机构：

[1] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea

[2] Busan Natl Univ Educ, Dept Math Educ, Busan 611736, South Korea

[3] Petr Gas Univ Ploiesti, Fac Econ Sci, Ploiesti 100680, Romania

[4] Univ Bucharest, Fac Math & Comp Sci, Res Ctr Geometry Topol & Algebra, Sect 1, Bucharest 70109, Romania

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2015年

关键词：

scalar curvature; mean curvature; delta-Casorati curvature; shape operator; quaternionic space form; slant submanifold; optimal inequality; QUATERNIONIC SPACE-FORMS; SLANT SUBMANIFOLDS;

D O I：

10.1186/s13660-015-0831-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we give a new proof for two sharp inequalities involving generalized normalized delta-Casorati curvatures of a slant submanifold in a quaternionic space form. These inequalities were recently obtained in Lee and Vilcu (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.

引用

页数：9