Abelian Complex Structures and Generalizations

TL;DR

This paper reviews the deformation theory of abelian complex structures, introduces semi-abelian generalized complex structures, and provides examples to illustrate this new concept.

Contribution

It proposes the novel concept of semi-abelian generalized complex structures and explores their properties and examples.

Findings

Introduction of semi-abelian generalized complex structures

Observations on properties of these structures

Examples illustrating the concept

Abstract

After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such structure and illustrate this new concept with a variety of examples.