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SCALAR CURVATURE OF CONTACT CR-SUBMANIFOLDS IN AN ODD-DIMENSIONAL UNIT SPHERE

  • Kim, Hyang-Sook (Department of Computational Mathematics School of Computer Aided Science Institute of Basic Science Inje University) ;
  • Pak, Jin-Suk (Department of Mathematics Education Kyungpook National University)
  • Received : 2008.12.04
  • Published : 2010.05.31

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

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Cited by

  1. HOMOLOGY OF CONTACT CR-WARPED PRODUCT SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE vol.52, pp.1, 2015, https://doi.org/10.4134/BKMS.2015.52.1.215