We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian G_{2} (\mathbb{C}^{m+2}). In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in G_{2} (\mathbb{C}^{m+2})satisfying such conditions., Eunmi Pak, Juan de Dios Pérez, Young Jin Suh., and Obsahuje seznam literatury
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.