Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians
We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian G 2(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(ℂ m+2) satisfying such conditions.
Keywordsreal hypersurface complex two-plane Grassmannian Hopf hypersurface Levi-Civita connection generalized Tanaka-Webster connection normal Jacobi operator
MSC 201053C40 53C15
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