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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