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arXiv · 2208.11897

New characterizations of ruled real hypersurfaces in complex projective space

Juan de Dios Pérez·David Pérez-López
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Abstract

We consider real hypersurfaces $M$ in complex projective space equipped with both the Levi-Civita and generalized Tanaka-Webster connections. For any nonnull constant $k$ and any symmetric tensor field of type (1,1) $L$ on $M$ we can define two tensor fields of type (1,2) on $M$, $L_F^{(k)}$ and $L_T^{(k)}$, related to both connections. We study the behaviour of the structure operator $\phi$ with respect to such tensor fields in the particular case of $L=A$, the shape operator of $M$, and obtain some new characterizations of ruled real hypersurfaces in complex projective space.

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Juan de Dios Pérez, David Pérez-López. 2022-08-25. New characterizations of ruled real hypersurfaces in complex projective space. https://arxiv.org/abs/2208.11897

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