On the Riemannian Curvature Tensor of a Real Hypersurface in Complex Two-Plane Grassmannians
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We prove the nonexistence of Hopf real hypersurfaces in complex two-plane Grassmannians such that the covariant derivatives with respect to Levi-Civita and kth generalized Tanaka–Webster connections in the direction of the Reeb vector field applied to the Riemannian curvature tensor coincide when the shape operator and the structure operator commute on the \(\mathcal Q\)-component of the Reeb vector field.
KeywordsReal hypersurfaces Complex two-plane Grassmannians Generalized Tanaka–Webster connection Riemannian curvature tensor Reeb vector field
Mathematics Subject ClassificationPrimary 53C40 Secondary 53C15
First author is partially supported by MCT-FEDER project MTM2013-47828-C2-1-P, and second author is supported by Fostering Core Leaders No. NRF-2013H1A8A1004325.
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