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Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator. (English) Zbl 1363.53049
Summary: 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.

MSC:
53C40 Global submanifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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