New characterizations of ruled real hypersurfaces in complex projective space

TL;DR

This paper introduces new characterizations of ruled real hypersurfaces in complex projective space by analyzing the behavior of the structure operator with respect to certain tensor fields related to both Levi-Civita and generalized Tanaka-Webster connections.

Contribution

It provides novel characterizations of ruled real hypersurfaces using tensor fields associated with both connections, expanding understanding of their geometric properties.

Findings

New characterizations of ruled real hypersurfaces

Behavior of the structure operator with respect to tensor fields

Relations between shape operator and connections

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.