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Ricci Curvature of Real Hypersurfaces in Non-flat Complex Space Forms

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Abstract

We establish an inequality among the Ricci curvature, the squared mean curvature, and the normal curvature for real hypersurfaces in complex space forms. We classify real hypersurfaces in two-dimensional non-flat complex space forms which admit a unit vector field satisfying identically the equality case of the inequality.

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  1. Division of Mathematics, Hachinohe Institute of Technology, Hachinohe, Aomori, 031-8501, Japan

    Toru Sasahara

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  1. Toru Sasahara
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Correspondence to Toru Sasahara.

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Sasahara, T. Ricci Curvature of Real Hypersurfaces in Non-flat Complex Space Forms. Mediterr. J. Math. 15, 141 (2018). https://doi.org/10.1007/s00009-018-1183-z

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  • DOI: https://doi.org/10.1007/s00009-018-1183-z

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