Contact 3-manifolds and Ricci solitons

TL;DR

This paper classifies contact 3-manifolds with transversal Ricci solitons, showing they are either Sasakian or locally isometric to specific Lie groups with left invariant metrics.

Contribution

It provides a classification of contact 3-manifolds admitting transversal Ricci solitons, identifying their geometric structures and associated Lie groups.

Findings

Contact 3-manifolds with transversal Ricci solitons are either Sasakian or locally isometric to certain Lie groups.

The Lie groups identified are SU(2), SL(2,R), E(2), and E(1,1).

These manifolds admit left invariant metrics compatible with the Ricci soliton structure.

Abstract

A contact 3-manifold $M$ admitting a transversal Ricci soliton $(g,v,\lambda)$ is either Sasakian or locally isometric to one of the Lie groups SU(2), $SL(2,R)$, E(2), E(1,1) with a left invariant metric.