Vaisman nilmanifolds

TL;DR

This paper characterizes compact nilmanifolds with Vaisman structures, showing they must be products of the Heisenberg group and the real line, thus classifying their geometric structure.

Contribution

It proves that the only compact nilmanifolds with Vaisman structures are those formed by the Heisenberg group times the real line, providing a complete classification.

Findings

Vaisman nilmanifolds are isomorphic to the product of the Heisenberg group and .

The structure of G in Vaisman nilmanifolds is explicitly characterized.

The classification of Vaisman nilmanifolds is achieved through this structural analysis.

Abstract

We prove that if a compact nilmanifold $\Gamma\backslash G$ is endowed with a Vaisman structure, then $G$ is isomorphic to the Cartesian product of the Heisenberg group with $\mathbb{R}$.