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Derivatives on Real Hypersurfaces of Non-flat Complex Space Forms

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Hermitian–Grassmannian Submanifolds

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 203))

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Abstract

Let M be a real hypersurface of a nonflat complex space form, that is, either a complex projective space or a complex hyperbolic space. On M we have the Levi-Civita connection and for any nonnull real number k the corresponding generalized Tanaka-Webster connection. Therefore on M we consider their associated covariant derivatives, the Lie derivative and, for any nonnull k, the so called Lie derivative associated to the generalized Tanaka-Webster connection and introduce some classifications of real hypersurfaces in terms of the concidence of some pairs of such derivations when they are applied to the shape operator of the real hypersurface, the structure Jacobi operator, the Ricci operator or the Riemannian curvature tensor of the real hypersurface.

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Acknowledgements

Author is partially supported by MINECO-FEDER Grant MTM2013-47828-C2-1-P.

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Authors and Affiliations

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

    Juan de Dios Pérez

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  1. Juan de Dios Pérez
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Correspondence to Juan de Dios Pérez .

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Editors and Affiliations

  1. Department of Mathematics and RIRCM, Kyungpook National University , Daegu, Korea (Republic of)

    Young Jin Suh

  2. Department of Mathematics and OCAMI, Osaka City University, Osaka, Japan

    Yoshihiro Ohnita

  3. School of Mathematics and Statistics, Southwest University, Chongqing, China

    Jiazu Zhou

  4. Department of Applied Mathematics, Kyung Hee University, Gyeonggi, Korea (Republic of)

    Byung Hak Kim

  5. Research Institute of Real and Complex Manifolds (RIRCM), Kyungpook National University, Daegu, Korea (Republic of)

    Hyunjin Lee

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de Dios Pérez, J. (2017). Derivatives on Real Hypersurfaces of Non-flat Complex Space Forms. In: Suh, Y., Ohnita, Y., Zhou, J., Kim, B., Lee, H. (eds) Hermitian–Grassmannian Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 203. Springer, Singapore. https://doi.org/10.1007/978-981-10-5556-0_3

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