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Bull. Korean Math. Soc. 2011; 48(3): 585-600

Printed May 1, 2011

https://doi.org/10.4134/BKMS.2011.48.3.585

Copyright © The Korean Mathematical Society.

Scalar curvature of contact three $CR$-submanifolds in a unit $(4m+3)$-sphere

Hyang Sook Kim and Jin Suk Pak

Inje University, Daegu University

Abstract

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In this paper we derive an integral formula on an $(n+3)$-dimensional, compact,minimal contact three $CR$-submanifold $M$ of $(p-1)$ contact three $CR$-dimension immersed in a unit $(4m+3)$-sphere $S^{4m+3}$. Using this integral formula, we give a sufficient condition concerning the scalar curvature of $M$ in order that such a submanifold $M$ is to be a generalized Clifford torus.

Keywords: unit (4m+3)-sphere, Sasakian $3$-structure, contact three $CR$-submanifold, scalar curvature

MSC numbers: 53C40, 53C25

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