Transitive Courant algebroids

Details Transitive Courant algebroids Transitive Courant algebroids

2004-07-23

arxiv.org/abs/math/0407399v1

Mathematics

Differential Geometry

LaTex, 27 pages

Scientific paper

We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal Whitney sum $E\oplus C$ 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.

Affiliated with

Also associated with

No associations

Rating

Transitive Courant algebroids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Transitive Courant algebroids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transitive Courant algebroids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-246402