A class of 3-dimensional contact metric manifolds

TL;DR

This paper classifies a specific class of 3-dimensional contact metric manifolds satisfying certain geometric conditions, advancing understanding of their structure.

Contribution

It provides a classification of contact metric 3-manifolds under particular gradient and covariant derivative conditions, which was previously unexplored.

Findings

Complete classification of the specified contact metric 3-manifolds.

Identification of geometric properties satisfying the given conditions.

Extension of known results in contact metric geometry.

Abstract

We classify the contact metric 3-manifolds that satisfy ||grad{\lambda}||=1 and \nabla_{{\xi}}{\tau}=2a{\tau}{\phi}.