• A Framedf (3,-1) Structure on the Cotangent Bundle of a Hamilton Space
Manuela Gîrtu
Abstract. 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 framedf (3,-1) structure P₂ of corank 2 naturally appears on T*M. This reduces to that found by us in [3] when H= K₂, for K the fundamental function of a Cartan space Kⁿ=(M, K). Then we show that on some conditions for H the restriction of P₂ to the submanifold H=1 of T^*₀M 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= K². The idea of this study has the origin in the paper [1] of M. Anastasiei.

2000 Mathematics Subject Classification: 53C60