Geodesic
Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 207-218

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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.
DOI : 10.1007/s10587-015-0169-2
Classification : 53C15, 53C40
Keywords: real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; generalized Tanaka-Webster connection; normal Jacobi operator; generalized Tanaka-Webster parallel normal Jacobi operator 
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Pak, Eunmi; de Dios Pérez, Juan; Machado, Carlos J. G.; Woo, Changhwa. Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 207-218. doi: 10.1007/s10587-015-0169-2

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