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On the Riemannian Curvature Tensor of a Real Hypersurface in Complex Two-Plane Grassmannians

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain

    Juan de Dios Pérez

  2. Department of Mathematics, Kyungpook National University, Daegu, 702-701, Republic of Korea

    Changhwa Woo

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  1. Juan de Dios Pérez
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  2. Changhwa Woo
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Correspondence to Juan de Dios Pérez.

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Communicated by See Keong Lee.

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Dios Pérez, J.d., Woo, C. On the Riemannian Curvature Tensor of a Real Hypersurface in Complex Two-Plane Grassmannians. Bull. Malays. Math. Sci. Soc. 42, 603–610 (2019). https://doi.org/10.1007/s40840-017-0500-1

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  • DOI: https://doi.org/10.1007/s40840-017-0500-1

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