Darboux theorem for generalized complex structures on transitive Courant algebroids

Abstract

Under natural assumptions we find local normal forms for generalized complex structures on transitive Courant algebroids, which extend Gualtieri's Darboux theorem for generalized complex structures on manifolds. When the base of the Courant algebroid is a point, they reduce to Wang's description of invariant complex structures on compact semisimple Lie groups.

31 pages. The main modifications with respect to the previous version are: Section 8 from the previous version is removed, the statement of the main result is simplified and we added Corollary 3. This is the final version accepted in Quart J Math