Generalized Moser lemma

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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 (⊗iE) ⊗ (⊗jE*) 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 languageEnglish (US)
Pages (from-to)5107-5123
Number of pages17
JournalTransactions of the American Mathematical Society
Volume362
Issue number10
DOIs
StatePublished - Oct 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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