Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2015; 52(5): 1631-1647

Printed September 1, 2015

https://doi.org/10.4134/BKMS.2015.52.5.1631

Copyright © The Korean Mathematical Society.

Optimal inequalities for the Casorati curvatures of submanifolds of generalized space forms endowed with semi-symmetric metric connections

Chul Woo Lee, Jae Won Lee, Gabriel-Eduard Vilcu, and Dae Won Yoon

Kyungpook National University, Busan National University of Education, Research Center in Geometry, Topology and Algebra, Gyeongsang National University

Abstract

In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.

Keywords: Casorati curvature, real space form, semi-symmetric metric connection

MSC numbers: 53C40, 49K35