# Manin Triples for Lie Bialgebroids

@article{Liu1995ManinTF, title={Manin Triples for Lie Bialgebroids}, author={Zhang-Ju Liu and Alan D. Weinstein and Ping Xu}, journal={Journal of Differential Geometry}, year={1995}, volume={45}, pages={547-574} }

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does not satisfy the Jacobi identity except on certain subspaces. In this paper we systematize the properties of this bracket in the definition of a Courant algebroid. This structure on a vector bundle $E\rightarrow M$, consists of an antisymmetric bracket on the sections of $E$ whose ``Jacobi anomaly…

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