Scalar curvature of contact $CR$-submanifolds in an odd-dimensional unit sphere
Bull. Korean Math. Soc. 2010 Vol. 47, No. 3, 541-549
https://doi.org/10.4134/BKMS.2010.47.3.541
Published online May 1, 2010
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
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