Complex and Kaehler structures on compact solvmanifolds

TL;DR

This paper investigates the existence and classification of complex and Kaehler structures on compact solvmanifolds, identifying all complex surfaces diffeomorphic to such manifolds and providing a comprehensive understanding of their geometric properties.

Contribution

It provides a complete classification of complex surfaces that are diffeomorphic to compact solvmanifolds, advancing the understanding of their geometric and topological structures.

Findings

All complex surfaces diffeomorphic to compact solvmanifolds are classified.

The paper characterizes the conditions for the existence of Kaehler structures on these manifolds.

Results contribute to the broader understanding of complex and Kaehler geometry on homogeneous spaces.

Abstract

We discuss our recent results on the existence and classification problem of complex and Kaehler structures on compact solvmanifolds. In particular, we determine in this paper all the complex surfaces which are diffeomorphic to compact solvmanifolds (and compact homogeneous manifolds in general).