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Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator

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Abstract

We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian G 2(ℂm+2) which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in G 2(ℂm+2) and prove non-existence of real hypersurfaces in G 2(ℂm+2) with generalized Tanaka-Webster parallel normal Jacobi operator.

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Authors and Affiliations

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

    Eunmi Pak & Changhwa Woo

  2. Departmento de Geometría y Topología, Faculta de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Juan de Dios Pérez & Carlos J. G. Machado

Authors
  1. Eunmi Pak
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  2. Juan de Dios Pérez
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  3. Carlos J. G. Machado
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  4. Changhwa Woo
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Corresponding author

Correspondence to Eunmi Pak.

Additional information

This work was supported by grant Proj. No. NRF-2011-220-C00002 from National Research Foundation of Korea. The first author was supported by grant Proj. No. NRF-2012-R1A2A2A-01043023, the second by MCT-FEDER Grant MTM 2010-18099 and the fourth by Proj. No. NRF-2013-H1A8A1004325.

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Pak, E., de Dios Pérez, J., Machado, C.J.G. et al. Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator. Czech Math J 65, 207–218 (2015). https://doi.org/10.1007/s10587-015-0169-2

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  • DOI: https://doi.org/10.1007/s10587-015-0169-2

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