### Abstract

We show how the classical Moser lemma from symplectic geometry extends to generalized complex structures (GCS) on arbitrary Courant algebroids. For this, we extend the notion of a Lie derivative to sections of the tensor bundle (⊗^{i}E) ⊗ (⊗^{j}E^{*}) with respect to sections of the Courant algebroid E using the Dorfman bracket. We then give a cohomological interpretation of the existence of one-parameter families of GCS on E and of flows of automorphims of E identifying all GCS of such a family. In the particular case of symplectic manifolds, we recover the results of Moser. Finally, we give a criterion to detect the local triviality of arbitrary GCS which generalizes the Darboux-Weinstein theorem.

Original language | English (US) |
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Pages (from-to) | 5107-5123 |

Number of pages | 17 |

Journal | Transactions of the American Mathematical Society |

Volume | 362 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2010 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

*Transactions of the American Mathematical Society*,

*362*(10), 5107-5123. https://doi.org/10.1090/S0002-9947-10-04965-2