It is shown that the general theory of lifting the tensor fields from a Riemannian manifold M to its tangent bundle TM enables one to define in a natural manner the unique sympletic connection on the phase space T?M which is induced by the Levi–Civita connection on M. This is exactly the symplectic connection given also by Bordemann, Neumaier and Waldmann Commun. Math. Phys. 198, 363 (1998); J. Geom. Phys. 29, 199 (1999). Relationship between the symplectic and Riemannian geometries on T?M and M is considered.
展开▼