Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator

Czechoslovak Mathematical Journal

Changhwa ¹  Eunmi Pak² 

[1] Carlos J. G. Machado, Departmento de Geometria y Topología, Faculta de Ciencias, Universidad de Granada, 18071-Granada, Spain;Changhwa Woo, Department of Mathematics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 702-701, Korea

关键词: real hypersurface;    complex two-plane Grassmannian;    Hopf hypersurface;    generalized Tanaka-Webster connection;    normal Jacobi operator;    generalized Tanaka-Webster parallel normal Jacobi operator;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian $G_2({\mathbb C}^{m+2})$ which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in $G_2({\mathbb C}^{m+2})$ and prove non-existence of real hypersurfaces in $G_2({\mathbb C}^{m+2})$ with generalized Tanaka-Webster parallel normal Jacobi operator.

【 授权许可】

Unknown