Mathematics – Differential Geometry
Scientific paper
2004-02-05
Mathematics
Differential Geometry
22 pages
Scientific paper
10.1088/0305-4470/37/24/010
Equipping the tangent bundle TQ of a manifold with a symplectic form coming from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis structure from a given type (1,1) tensor field J on Q. It is argued that the complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ, but plays a crucial role in the construction of a different tensor R, which appears to be the pullback under the Legendre transform of the lift of J to co-tangent manifold of Q. We show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle, in the case that Q is equipped with a Riemannian metric. The present approach further paves the way for future generalizations.
Sarlet Willy
Vermeire F.
No associations
LandOfFree
A class of Poisson-Nijenhuis structures on a tangent bundle 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 A class of Poisson-Nijenhuis structures on a tangent bundle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A class of Poisson-Nijenhuis structures on a tangent bundle will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-318682