Moser Lemma in Generalized Complex Geometry

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 Lie derivative to sections of the tensor bundle $({\otimes }^{i}E)\otimes ({\otimes }^j{E}^{\ast })$ 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 cases of symplectic, 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.

18 pages

References in corpus (9)

• Reduction of Courant algebroids and generalized complex structures
• Generalized complex geometry
• Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
• New aspects of the ddc-lemma
• Generalized geometry and the Hodge decomposition
• Hamiltonian symmetries and reduction in generalized geometry
• A surgery for generalized complex structures on 4-manifolds
• Formality in generalized Kahler geometry
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Cited by in corpus (1)

• LA-Courant algebroids and their applications