Almost abelian complex nilmanifolds

TL;DR

This paper proves the uniqueness of complex structures on almost abelian nilpotent Lie algebras and explores their cohomology and deformation properties, providing comprehensive insights into their geometric structure.

Contribution

It establishes the uniqueness of complex structures on almost abelian nilpotent Lie algebras and analyzes their cohomology and deformation characteristics.

Findings

Uniqueness of complex structures on almost abelian nilpotent Lie algebras.

Complete understanding of cohomology for these manifolds.

Insights into deformation theory of almost abelian complex nilmanifolds.

Abstract

We show that a complex structure on a nilpotent almost abelian real Lie algebra is unique if it exists. As a consequence, we get full control over the cohomology and deformations of almost abelian complex nilmanifolds.