Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2010; 47(3): 541-549

Printed May 1, 2010

https://doi.org/10.4134/BKMS.2010.47.3.541

Copyright © The Korean Mathematical Society.

Scalar curvature of contact $CR$-submanifolds in an odd-dimensional unit sphere

Hyang Sook Kim and Jin Suk Pak

Inje University and Kyungpook National University

Abstract

In this paper we derive an integral formula on an $(n+1)$-dimensional, compact, minimal contact $CR$-submanifold $M$ of $(n-1)$ contact $CR$-dimension immersed in a unit $(2m+1)$-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of $M$ in order that such a submanifold $M$ is to be a generalized Clifford torus.

Keywords: Sasakian manifold, odd-dimensional unit sphere, contact $CR$-submanifold, scalar curvature

MSC numbers: 53C40, 53C15