Tulczyjew's Triplet with an Ehresmann connection I: Trivialization and Reduction

Abstract

We study the trivialization and the reduction of the Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus obtain trivializations and reductions of iterated tangent and cotangent bundles $T^{\ast }TQ$, $T{T}^{\ast }Q$ and $T^{\ast }{T}^{\ast }Q$. Accordingly, the symplectomorphisms between these manifolds are properly trivialized and reduced.

Cited by in corpus (1)

• Tulczyjew's Triplet for Lie Groups III : Higher Order Dynamics and Reductions for Iterated Bundles