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Parallelism of Structure Lie Operators on Real Hypersurfaces in Nonflat Complex Space Forms

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Abstract

In this paper, it is proved that the structure Lie operator of a real hypersurface in a nonflat complex space form is parallel with respect to the generalized Tanaka–Webster connection if and only if it vanishes identically, and hence, this is equivalent to that the real hypersurface is of type (A).

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Acknowledgements

The authors would like to express their gratitude to the reviewer for careful reading and valuable suggestions.

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  1. School of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Yaning Wang & Pei Wang

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  1. Yaning Wang
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Correspondence to Yaning Wang.

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Wang, Y., Wang, P. Parallelism of Structure Lie Operators on Real Hypersurfaces in Nonflat Complex Space Forms. Mediterr. J. Math. 21, 8 (2024). https://doi.org/10.1007/s00009-023-02551-7

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