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Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians

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Abstract

We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian G 2(ℂm+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(ℂm+2) satisfying such conditions.

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Authors and Affiliations

  1. Department of Mathematics, Kyungpook National University, 80 Daehakro, Bugku, Daegu, 702-701, Republic of Korea

    Eunmi Pak & Young Jin Suh

  2. Departmento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, Campus de Fuentenueva s/n, 18071, Granada, Spain

    Juan de Dios Pérez

Authors
  1. Eunmi Pak
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  2. Juan de Dios Pérez
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  3. Young Jin Suh
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Corresponding author

Correspondence to Eunmi Pak.

Additional information

This work was supported by grant Proj. No. NRF-2015-R1A2A1A-01002459 from National Research Foundation. The second author is partially supported by MCT-FEDER Grant MTM2010-18099.

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Pak, E., de Dios Pérez, J. & Suh, Y.J. Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians. Czech Math J 65, 569–577 (2015). https://doi.org/10.1007/s10587-015-0196-z

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  • DOI: https://doi.org/10.1007/s10587-015-0196-z

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