Generalized Moser lemma

Research output: Contribution to journalArticle

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 1 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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