13 research outputs found
Moser Lemma in Generalized Complex Geometry
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
with respect to sections of the Courant
algebroid using the Dorfman bracket. We then give a cohomological
interpretation of the existence of one-parameter families of GCS on and of
flows of automorphims of 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.Comment: 18 page
On Regular Courant Algebroids
For any regular Courant algebroid, we construct a characteristic class a la
Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3
class in its naive cohomology. When the Courant algebroid is exact, it reduces
to the Severa class (in H^3_{DR}(M)). On the other hand, when the Courant
algebroid is a quadratic Lie algebra g, it coincides with the class of the
Cartan 3-form (in H^3(g)). We also give a complete classification of regular
Courant algebroids and discuss its relation to the characteristic class.Comment: Section 3.3 and references added; An error about classification is
correcte