Geometric structures on the tangent bundle of the Einstein spacetime

Josef Janyska

Address.
Department of Mathematics, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic

E-mail: janyska@math.muni.cz

Abstract.
We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bunde of the Einstein spacetime

AMSclassification. 53B15, 53B30, 53D05, 53D17, 58A10, 58A20, 58A32.

Keywords. Spacetime, spacetime connection, Schouten bracket,Fr\"olicher--Ni\-jen\-huis bracket, symplectic structure, Poisson structure