Kenmotsu LIe groups

TL;DR

This paper classifies connected, simply-connected Lie groups with left-invariant Kenmotsu structures and shows they are Einstein Riemannian manifolds, contributing to the understanding of contact geometry and Lie group structures.

Contribution

It provides a complete classification of Lie groups with left-invariant Kenmotsu structures and proves their Einstein property, which was previously unknown.

Findings

Classified all connected, simply-connected Lie groups with Kenmotsu structures.

Proved these Lie groups are Einstein Riemannian manifolds.

Enhanced understanding of contact geometry on Lie groups.

Abstract

Kenmotsu manifolds constitute an important subclass of the class of contact Riemannian manifolds. In this note, we determine entirely connected and simply-connected Lie groups having a left invariant Kenmotsu structure. We show also that these Lie groups are Einstein Riemannian manifolds.