An almost 2-paracontact structure on the cotangent bundle of a Cartan space

Abstract

A Cartan space is a pair (M, K), where M is a smooth manifold and K an Hamiltonean on the slit cotangent bundle $T_0^{star}$ M := TM{(x, 0), x$in$ M}, that is positively homogeneous of degree 1 in momenta. We show that K induces an almost 2-paracontact Riemannian structure on $T_0^{star} M whose restriction to the figuratrix bundle $Bbb{K}$ = {(x,p) K(x,p) = 1} is an almost paracontact structure. A condition for this almost para-contact structure to be normal is found, and its geometrical meaning is pointed out. Similar results for Finsler spaces can be found in [1] and [3].