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Keywords:
real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; Levi-Civita connection; generalized Tanaka-Webster connection; normal Jacobi operator
Summary:
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.
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