Almost Paracontact Structures and Time Dependent Lagrangians

Let M be a smooth manifold and TM its tangent bundle. We associate to a nonlinear connection in the vector bundle £ • ^ x TM -» SR x M an ^^g^ paracontact structure on ^ x TM _ ^ js well-known ([1],[3]) that any regular time dependent Lagrangian -L'^x TM —> SR defines a nonlinear connection in the vector bundle , an almost paracontact structure depending on L is obtained. Several properties of it are pointed out.