Courant algebroids which are not exact - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T08:05:21Z http://mathoverflow.net/feeds/question/110007 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110007/courant-algebroids-which-are-not-exact Courant algebroids which are not exact Benjamin 2012-10-18T11:52:14Z 2012-10-18T13:57:59Z <p>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 $H$.</p> <p>Thank you!</p> http://mathoverflow.net/questions/110007/courant-algebroids-which-are-not-exact/110013#110013 Answer by Eugene Lerman for Courant algebroids which are not exact Eugene Lerman 2012-10-18T13:57:59Z 2012-10-18T13:57:59Z <p>The answer depends on what you mean by interesting."</p> <p>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 $TM\oplus T^*M \to M$.</p> <p>Grützmann's thesis (arXiv:1004.1487 [math.DG]) maybe another good place to look.</p>