Non Kaehler solvmanifolds with generalized Kaehler structure

TL;DR

This paper constructs a 6-dimensional solvmanifold with a non-trivial invariant generalized Kähler structure that is not Kähler, highlighting differences from nilmanifolds which cannot admit such structures unless they are tori.

Contribution

It provides the first example of a compact solvmanifold with a non-trivial invariant generalized Kähler structure that is not Kähler.

Findings

Constructed a 6-dimensional solvmanifold with generalized Kähler structure

Demonstrated the manifold does not admit any Kähler metric

Contrasted with nilmanifolds which cannot have such structures unless tori

Abstract

We construct a compact 6-dimensional solvmanifold endowed with a non-trivial invariant generalized K\"ahler structure and which does not admit any K\"ahler metric. This is in contrast with the case of nilmanifolds which cannot admit any invariant generalized K\"ahler structure unless they are tori.