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.

References in corpus (4)

• Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
• Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds
• Weak Mirror Symmetry of Complex Symplectic Algebras
• A Hodge-Type Decomposition of Holomorphic Poisson Cohomology on Nilmanifolds