Scalar curvature of contact three $CR$-submanifolds in a unit $(4m+3)$-sphere
Bull. Korean Math. Soc. 2011 Vol. 48, No. 3, 585-600
Published online May 1, 2011
Hyang Sook Kim and Jin Suk Pak
Inje University, Daegu University
Abstract : 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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