Small deformations and non-left-invariant complex structures on a compact solvmanifold

Abstract

We observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds, including tori, are left-invariant. In this paper we will give an example of a six-dimensional compact solvmanifold which admits a continuous family of non-left-invariant complex structures. Furthermore, we will make a complete classification of three-dimensional compact homogeneous complex solvmanifolds; and determine which of them admit pseudo-Kaehler structures.

11 pages; revised version with a more detailed proof for the main theorem

Cited by in corpus (1)

• Complex and Kaehler structures on compact homogeneous manifolds - their existence, classification and moduli problem