Sectional curvature of contact $CR$-submanifolds of an odd-dimensional unit sphere

摘要

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 $$ S^{2n_1 +1}(((2n_1 +1)/(n+1))^{rac{1}{2}})imes S^{2n_2 +1}(((2n_2 +1)/(n+1))^{rac{1}{2}}) $$ for some portion $(n_1 ,n_2)$ of $(n-1)/2$ in terms with sectional curvature.