258 research outputs found
Transitive Courant algebroids
We express any Courant algebroid bracket by means of a metric connection, and
construct a Courant algebroid structure on any orthogonal Whitney sum where E is a given Courant algebroid and C is a flat, pseudo- Euclidean
vector bundle. Then, we establish the general expression of the bracket of a
transitive Courant algebroid, i.e., a Courant algebroid with a surjective
anchor, and describe a class of transitive Courant algebroids which are Whitney
sums of a Courant subalgebroid with neutral metric and Courant-like bracket and
a pseudo-Euclidean vector bundle with a flat, metric connection. In particular,
this class contains all the transitive Courant algebroids of minimal rank; for
these, the flat term mentioned above is zero. The results extend to regular
Courant algebroids, i.e., Courant algebroids with a constant rank anchor. The
paper ends with miscellaneous remarks and an appendix on Dirac linear spaces.Comment: LaTex, 27 page
AV-Courant algebroids and generalized CR structures
We construct a generalization of Courant algebroids which are classified by
the third cohomology group , where is a Lie Algebroid, and is
an -module. We see that both Courant algebroids and
structures are examples of them. Finally we introduce generalized CR structures
on a manifold, which are a generalization of generalized complex structures,
and show that every CR structure and contact structure is an example of a
generalized CR structure.Comment: 18 page
Twisted Courant algebroids and coisotropic Cartan geometries
In this paper, we show that associated to any coisotropic Cartan geometry
there is a twisted Courant algebroid. This includes in particular parabolic
geometries. Using this twisted Courant structure, we give some new results
about the Cartan curvature and the Weyl structure of a parabolic geometry. As
more direct applications, we have Lie 2-algebra and 3D AKSZ sigma model with
background associated to any coisotropic Cartan geometry
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
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