Take the tour ×  Does somebody have some interesting examples of
Courant algebroids which are not exact? By exact I mean one
which is of the form $TM\oplus T^\star M$ with the standard
bracket twisted by a closed 3-form $H$.  Thank you!
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down vote accepted  The answer depends on what you mean by
``interesting."  For example the paper "On the Geometric
Structure of Hamiltonian Systems with Ports" by Jochen Merker, J
Nonlinear Sci (2009) 19: 717–738 DOI 10.1007/s00332-009-9052-3,
may be considered as dealing with interesting examples of
Courant algebroids. The algebroids there are not of the form
$TM\oplus T^*M \to M$.  Grützmann's thesis (arXiv:1004.1487
[math.DG]) maybe another good place to look.  share|improve this
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