A Framedf(3,-1) Structure on the Cotangent Bundle of a Hamilton Space

Manuela Gîrtu

Bulletin of the Malaysian Mathematical Society, Tome 27 (2004) no. 2

Résumé

For the cotangent bundle ( T * M , τ * , M ) of a smooth manifold M , the kernel of a differential τ * * of the projection τ * defines the vertical subbundle VT * M of the bundle ( TT * M , τ T * M , T * M ). A supplement HT * M of it is called a horizontal subbundle or a nonlinear connection on M , [6,7]. The direct decomposition TT * M = HT * M Å VT * M gives rise to a natural almost product structure P on the manifold T * M . A general method to associate to P a framed f (3,-1) structure of any corank is pointed out. This is similar to that given by us in [2] for the tangent bundle of a Lagrange space. When we endow M with a regular Hamiltonian H and use as the nonlinear connection that canonically induced by H , a framed f (3,-1) structure P 2 of corank 2 naturally appears on T * M . This reduces to that found by us in [3] when H = K 2 , for K the fundamental function of a Cartan space K n =( M , K ). Then we show that on some conditions for H the restriction of P 2 to the submanifold H =1 of T * 0 M provides an almost paracontact structure on this submanifold. The conditions taken on H hold for the f -Hamiltonians introduced by us in [4] as well as for H = K 2 . The idea of this study has the origin in the paper [1] of M. Anastasiei.

Détail

Classification : 53C60