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# AV-Courant Algebroids and Generalized CR Structures

Published:2011-02-25
Printed: Aug 2011
• David Li-Bland,
Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4
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## Abstract

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.
 MSC Classifications: 53D18 - Generalized geometries (a la Hitchin)

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