Nullity distributions on real hypersurfaces in non-flat complex space forms

TL;DR

This paper extends the study of nullity distributions on real hypersurfaces in non-flat complex space forms, introducing new generalized notions and analyzing the properties of hypersurfaces with structure vector fields in these distributions.

Contribution

It generalizes nullity distribution concepts to three-dimensional hypersurfaces and introduces the ($ppa$,$mu$,$nu$)-nullity distribution, providing new classifications and results.

Findings

Extended nullity distribution results to 3D hypersurfaces.

Introduced and studied ($ppa$,$mu$,$nu$)-nullity distribution.

Provided classifications of hypersurfaces with structure vector fields in these distributions.

Abstract

In this paper the result of real hypersurfaces in non-flat complex space forms, whose structure vector field $\xi$ belongs to the $\kappa$-nullity distribution is extended in case of three dimensional real hypersurfaces in non-flat complex space forms. Furthermore, generalization of notion ($\kappa$,$\mu$)-nullity distribution defined on real hypersurfaces and results of real hypersurfaces, whose structure vector field $\xi$ belongs to the previous distribution are provided. Finally, the notion of ($\kappa$,$\mu$,$\nu$)-nullity distribution is introduced in case of real hypersurfaces in non-flat complex space forms and real hypersurfaces, whose structure vector field $\xi$ belongs to the previous distribution are studied.