AV-Courant algebroids and generalized CR structures

Details AV-Courant algebroids and generalized CR structures AV-Courant algebroids and generalized CR structures

2008-11-28

arxiv.org/abs/0811.4470v2

Canadian Journal of Mathematics, 63(4):pp. 938-960 (2011)

Mathematics

Differential Geometry

18 pages

Scientific paper

10.4153/CJM-2011-009-1

We construct a generalization of Courant algebroids which 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.

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