Homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups

TL;DR

This paper classifies simply connected homogeneous Sasaki and Vaisman manifolds arising from unimodular Lie groups, revealing their structure and providing a comprehensive classification up to modification.

Contribution

It offers a structure theorem and a complete classification of simply connected homogeneous Sasaki and Vaisman manifolds on unimodular Lie groups.

Findings

Established a basic structure theorem for these manifolds.

Provided a complete classification up to modification.

Connected the geometry of Vaisman manifolds with unimodular Lie groups.

Abstract

A Vaisman manifold is a special kind of locally conformally Kaehler manifold, which is closely related to a Sasaki manifold. In this paper we show a basic structure theorem of simply connected homogeneous Sasaki and Vaisman manifods of unimodular Lie groups, up to holomorphic isometry. For the case of unimodular Lie groups, we obtain a complete classification of simply connected Sasaki and Vaisman unimodular Lie groups, up to modification.