Compatible structures on Lie algebroids and Monge-Ampère operators

Details Compatible structures on Lie algebroids and Monge-Ampère operators Compatible structures on Lie algebroids and Monge-Ampère operators

2008-12-30

arxiv.org/abs/0812.4838v1

Mathematics

Differential Geometry

To be published in Acta. Appl. Math, 2009

Scientific paper

We study pairs of structures, such as the Poisson-Nijenhuis structures, on the tangent bundle of a manifold or, more generally, on a Lie algebroid or a Courant algebroid. These composite structures are defined by two of the following, a closed 2-form, a Poisson bivector or a Nijenhuis tensor, with suitable compatibility assumptions. We establish the relationships between such composite structures. We then show that the non-degenerate Monge-Amp\`ere structures on 2-dimensional manifolds satisfying an integrability condition provide numerous examples of such structures, while in the case of 3-dimensional manifolds, such Monge-Amp\`ere operators give rise to generalized complex structures or generalized product structures on the cotangent bundle of the manifold.

Affiliated with

Also associated with

No associations

Rating

Compatible structures on Lie algebroids and Monge-Ampère operators 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 Compatible structures on Lie algebroids and Monge-Ampère operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Compatible structures on Lie algebroids and Monge-Ampère operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-117188