General Mathematics, Vol. 5, No. 1 - 4, pp. 255-266, 1995

Gabriel Mitric

Abstract: Considering some regular geometric objects on the tangent and cotangent bundles of a smooth manifold $M$, we define some diffeomorphisms between these bundles, which establish some relations between the mechanical structures on $TM$ and $T^{*}M$. We construct a mechanical structure on $T^{*}M$ and we also study the condition under which a regular vector field defining a mechanical structure on $T^{*}M$ is a semi-Hamilton or Hamilton vector field.

Classification (MSC91): 53C05, 53C15, 58F5.

Keywords: tangent and cotangent bundle, spray, regular vector field, nonlinear connection, mechanical structure.

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