AV-Courant Algebroids and Generalized CR Structures

http://dx.doi.org/10.4153/CJM-2011-009-1
Canad. J. Math. 63(2011), 938-960

  Published:2011-02-25
 Printed: Aug 2011

We construct a generalization of Courant algebroids that are classified by the third cohomology group $H^3(A,V)$, where $A$ is a Lie Algebroid, and $V$ is an $A$-module. We see that both Courant algebroids and $\mathcal{E}^1(M)$ 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.