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AV-Courant Algebroids and Generalized CR Structures

Published online by Cambridge University Press:  20 November 2018

David Li-Bland
David Li-Bland*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4 e-mail: david.libland@gmail.com
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Abstract

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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 ${{\text{ }\!\!\varepsilon\!\!\text{ }}^{1}}(M)$ structures are examples of them. Finally we introduce generalized $\text{CR}$ structures on a manifold, which are a generalization of generalized complex structures, and show that every $\text{CR}$ structure and contact structure is an example of a generalized $\text{CR}$ structure.

Keywords

53D18
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 4 , 01 August 2011 , pp. 938 - 960
Copyright
Copyright © Canadian Mathematical Society 2011

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