Geometrical structures on the cotangent bundle (Q2805593)

Global differential geometry and topological methods are the effective tools in qualitative investigations of the analytical mechanics problems, especially connected with vector fields of Hamiltonian and Lagrangian systems. It is well known that many geometric structures on the cotangent bundle \(T^*M\) of a differentiable manifold \(M\) can be studied using the same methods as in the case of the tangent bundle \(TM\). The tangent bundle has a naturally defined integrable tangent structure that together with a semispray (second-order differential equation vector field) induces a nonlinear connection. Here, more geometrical structures on the cotangent bundle are investigated and it is shown how the dynamical covariant derivative induced by a regular vector field and an arbitrary nonlinear connection fix the nonlinear connection.