Sectional curvature of contact $CR$-submanifolds of an odd-dimensional unit sphere
Bull. Korean Math. Soc. 2005 Vol. 42, No. 4, 777-787
Published online December 1, 2005
Hyang Sook Kim and Jin Suk Pak
Inje University, Kyungpook National University
Abstract : In this paper we study $(n+1)$-dimensional compact contact $CR$-submanifolds of $(n-1)$ contact $CR$-dimension immersed in an odd-dimensional unit sphere $S^{2m+1}$. Especially we provide necessary conditions in order for such a submanifold to be the generalized Clifford surface $$ S^{2n_1 +1}(((2n_1 +1)/(n+1))^{\frac{1}{2}})\times S^{2n_2 +1}(((2n_2 +1)/(n+1))^{\frac{1}{2}}) $$ for some portion $(n_1 ,n_2)$ of $(n-1)/2$ in terms with sectional curvature.
Keywords : Sasakian manifold, odd-dimensional unit sphere, contact $CR$-submanifold, contact $CR$-dimension, minimal real hypersurface, sectional curvature
MSC numbers : 53C40, 53C15
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd