Covariant almost analytic vector field on Q - Quasi umbilical hypersurface of a Sasakian manifold

TL;DR

This paper investigates the properties of covariant almost analytic vector fields on Q-quasi umbilical hypersurfaces within Sasakian manifolds, deriving conditions for the hypersurface to be totally umbilical or cylindrical.

Contribution

It introduces new conditions involving covariant almost analytic vector fields that characterize the geometric nature of Q-quasi umbilical hypersurfaces in Sasakian manifolds.

Findings

Derived scalars α and β related to the hypersurface structure.

Established conditions for hypersurface to be totally umbilical.

Identified criteria for hypersurface to be cylindrical.

Abstract

In this paper we have studied the properties of covariant almost analytic vector field on Q - quasi umbilical hypersurface $M$ of a Sasakian manifold $\tilde M$ with $(\phi, g, u, v, \lambda)-$structure and obtained the scalars $\alpha$ and $\beta$ using $1 - form u, v$ covariant almost analytic for the hypersurface $M$ to be totally umbilical and cylindrical.