Geometrical structures on the cotangent bundle

Abstract

In this paper we study the geometrical structures on the cotangent bundle using the notions of adapted tangent structure and regular vector fields. We prove that the dynamical covariant derivative on $T^{\ast }M$ fix a nonlinear connection for a given $\mathcal{J}$-regular vector field. Using the Legendre transformation induced by a regular Hamiltonian, we show that a semi-Hamiltonian vector field on $T^{\ast }M$ corresponds to a semispray on $TM$ if and only if the nonlinear connection on $TM$ is just the canonical nonlinear connection induced by the regular Lagrangian.

International Journal of Geometric Methods in Modern Physics, 2016

References in corpus (2)

• Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations
• A geometric setting for systems of ordinary differential equations