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.
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页数：9
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