Geodesic
Geometric structures on the tangent bundle of the Einstein spacetime
Archivum mathematicum, Tome 42 (2006) no. 2, pp. 195-203.

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We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.
Classification : 53B15, 53B30, 53D05, 53D17
Keywords: spacetime; spacetime connection; Schouten bracket; Frölicher–Nijenhuis bracket; symplectic structure; Poisson structure 
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     title = {Geometric structures on the tangent bundle of the {Einstein} spacetime},
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Janyška, Josef. Geometric structures on the tangent bundle of the Einstein spacetime. Archivum mathematicum, Tome 42 (2006) no. 2, pp. 195-203. http://geodesic.mathdoc.fr/item/ARM_2006__42_2_a10/