Abelian Complex Structures and Generalizations

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.

Keywords

• abelian complex structures
• deformation
• nilmanifolds
• primary 53d18
• secondary 32g07, 14d15, 17b30, 17b62