On a class of paracontact metric 3-manifolds

TL;DR

This paper classifies 3-dimensional paracontact metric manifolds where the Ricci operator commutes with the structure endomorphism, advancing understanding of their geometric properties.

Contribution

It provides a classification of paracontact metric 3-manifolds based on the commutation of Ricci operator and structure endomorphism.

Findings

Classification of such manifolds achieved

Conditions for Ricci operator and endomorphism to commute identified

New insights into the structure of paracontact metric 3-manifolds

Abstract

The purpose of this paper is to classify paracontact metric $3$-manifolds $M^3$ such that the Ricci operator $S$ commutes with the endomorhism $\phi$ of its tangent bundle $\Gamma(TM^3)$.