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Curvature of Hopf Hypersurfaces in a Complex Space Form

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Abstract

We study curvature of Hopf hypersurfaces in a complex projective space or hyperbolic space. In particular, we prove that there are no real hypersurfaces in a non-flat complex space form whose Reeb-sectional curvature vanishes.

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Authors and Affiliations

  1. Department of Mathematics, Chonnam National University, Gwangju, 500-757, Korea

    Jong Taek Cho

  2. Department of Mathematics, Faculty of Science and Engineering, Shimane University, Matsue, Shimane, 690-8504, Japan

    Makoto Kimura

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  1. Jong Taek Cho
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  2. Makoto Kimura
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Correspondence to Jong Taek Cho.

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Cho, J.T., Kimura, M. Curvature of Hopf Hypersurfaces in a Complex Space Form. Results. Math. 61, 127–135 (2012). https://doi.org/10.1007/s00025-010-0080-y

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  • DOI: https://doi.org/10.1007/s00025-010-0080-y

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