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Real Hypersurfaces in the Complex Quadric with Reeb Parallel Ricci Tensor

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Abstract

First we introduce the notion of commuting and parallel Ricci tensor for real hypersurfaces in the complex quadric \(Q^m = SO_{m+2}/SO_2SO_m\). Then, according to the \(\mathfrak {A}\)-principal or the \(\mathfrak {A}\)-isotropic unit normal vector field N, respectively, we give a classification of real hypersurfaces in \(Q^m = SO_{m+2}/SO_2SO_m\) with Reeb parallel Ricci tensor.

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Acknowledgements

The present author would like to express his deep gratitude to the referee for his/her careful comments and suggestions throughout our manuscript. By virtue of his/her best efforts, we can make good expressions better than the previous one.

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Authors and Affiliations

  1. Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu, 41566, Republic of Korea

    Young Jin Suh

  2. Research Institute of Real & Complex Manifolds, Kyungpook National University, 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 Quadric with Reeb Parallel Ricci Tensor. J Geom Anal 29, 3248–3269 (2019). https://doi.org/10.1007/s12220-018-00113-y

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  • DOI: https://doi.org/10.1007/s12220-018-00113-y

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