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Real Hypersurfaces in the Complex Hyperbolic Quadric with Parallel Normal Jacobi Operator

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Abstract

First, we introduce the notion of parallel normal Jacobi operator for real hypersurfaces in the complex hyperbolic quadric \({Q^m}^* = SO_{m,2}/SO_mSO_2\). Next we give a complete proof of non-existence of real hypersurfaces in \({Q^m}^* = SO_{m,2}/SO_mSO_2\) with parallel normal Jacobi operator.

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Authors and Affiliations

  1. Department of Mathematics, Kyungpook National University & RIRCM, Daegu, 41566, Republic of Korea

    Young Jin Suh

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  1. Young Jin Suh
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Correspondence to Young Jin Suh.

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This work was supported by Grant Proj. no. NRF-2018-R1D1A1B-05040381 from National Research Foundation of Korea.

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Suh, Y.J. Real Hypersurfaces in the Complex Hyperbolic Quadric with Parallel Normal Jacobi Operator. Mediterr. J. Math. 15, 159 (2018). https://doi.org/10.1007/s00009-018-1202-0

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  • DOI: https://doi.org/10.1007/s00009-018-1202-0

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