Some curvature restrictions on $3$-dimensional generalized ($\kappa ,\mu $)-contact metric manifolds

TL;DR

This paper investigates specific curvature conditions on 3-dimensional generalized ($rac,rac$)-contact metric manifolds, aiming to classify these manifolds under certain geometric restrictions.

Contribution

It provides a classification of 3D generalized ($rac,rac$)-contact metric manifolds satisfying particular curvature conditions, extending previous classifications.

Findings

Classified manifolds under $ ilde{W}ullet R=0$ and $ ilde{W}ullet H=0$ conditions.

Covered all eight equivalent classes from prior work.

Enhanced understanding of curvature restrictions in contact metric geometry.

Abstract

The object of the present study is to study 3-dimensional generalized ($\kappa ,\mu $)-contact metric manifolds with $\tilde{W}\cdot R=0$ and $\tilde{W}\cdot H=0$ to cover all the eight equivalent classes given in \cite{Shaikh2}.