zbMATH — the first resource for mathematics

Natural symplectic structures on the tangent bundle of a space-time. (English) Zbl 0908.53017
Slovák, Jan (ed.), Proceedings of the 15th Winter School on geometry and physics, Srní, Czech Republic, January 14–21, 1995. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43, 153-162 (1996).
In this nice paper the author proves that all natural symplectic forms on the tangent bundle of a pseudo-Riemannian manifold are pull-backs of the canonical symplectic form on the cotangent bundle with respect to some diffeomorphisms which are naturally induced by the metric.
For the entire collection see [Zbl 0884.00042].

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics