AV-Courant Algebroids and Generalized CR Structures

Abstract

Abstract We construct a generalization of Courant algebroids that are classified by the third coho- mology group H3(A , V), where A is a Lie Algebroid, and V is an A-module. We see that both Courant algebroids and structures are examples of them. Finally we introduce generalized CR structures on a manifold, which are a generalization of generalized complex structures, and show that every CR structure and contact structure is an example of a generalized CR structure.