On the curvature symmetries in lightlike hypersurfaces of an indefinite Sasakian manifold

TL;DR

This paper investigates the geometric properties of lightlike hypersurfaces within indefinite Sasakian manifolds, demonstrating that those tangent to the structure vector field lack certain symmetry properties such as local symmetry, semi-symmetry, or semi-parallelism.

Contribution

It establishes that lightlike hypersurfaces tangent to the structure vector field in indefinite Sasakian manifolds do not exhibit local symmetry, semi-symmetry, or semi-parallelism, highlighting specific geometric constraints.

Findings

Lightlike hypersurfaces tangent to the structure vector field are not locally symmetric.

Such hypersurfaces are not semi-symmetric.

They are also not semi-parallel.

Abstract

In this note, we show that a lightlike hypersurface of an indefinite Sasakian manifold, which is tangent to structure vector field is not locally symmetric, semi-symmetric or semi-parallel.