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On a Class of Real Hypersurfaces in a Complex Space Form with Weakly \(\phi \)-Invariant Shape Operator

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Abstract

In this paper, we study real hypersurfaces in a complex space form with weakly \(\phi \)-invariant shape operator, where \(\phi \) is the almost contact structure on the real hypersurfaces induced by the complex structure on its ambient space. We first construct a class of real hypersurfaces with weakly \(\phi \)-invariant shape operator in complex Euclidean spaces and complex projective spaces and then give a characterization of such a class of real hypersurfaces. With this results, we classify minimal real hypersurfaces with weakly \(\phi \)-invariant shape operator in complex Euclidean spaces and in complex projective spaces.

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Acknowledgments

This work was supported in part by the UMRG research Grant (Grant No. RG163/11AFR)

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  1. Institute of Mathematical Sciences, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Tee-How Loo

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  1. Tee-How Loo
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Correspondence to Tee-How Loo.

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Communicated by Young Jin Suh.

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Loo, TH. On a Class of Real Hypersurfaces in a Complex Space Form with Weakly \(\phi \)-Invariant Shape Operator. Bull. Malays. Math. Sci. Soc. 38, 1297–1316 (2015). https://doi.org/10.1007/s40840-014-0076-y

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  • DOI: https://doi.org/10.1007/s40840-014-0076-y

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