Janyška, Josef; Modugno, Marco Geometric structures of the classical general relativistic phase space. (English) Zbl 1160.53008 Int. J. Geom. Methods Mod. Phys. 5, No. 5, 699-754 (2008). The paper is devoted to the study of geometric properties of the phase space, which is interpreted as the first jet space of motions regarded as time-like one-dimensional submanifolds of space-time. In particular, the authors study the contact and Jacobi structures induced by the Lorentz metric. It is also shown that the electromagnetic field yields additional terms to the purely geometric objects of the phase space. The conditions are determined under which the geometric objects induced on the phase space by a general phase connection yield contact and Jacobi structures. A useful tool in such investigations is the geometry of jets of submanifolds and the theory of natural differential operators. Reviewer: Miroslav Doupovec (Brno) Cited in 6 Documents MSC: 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 53B15 Other connections 53D05 Symplectic manifolds (general theory) 53D17 Poisson manifolds; Poisson groupoids and algebroids 58A10 Differential forms in global analysis 58A20 Jets in global analysis 58A32 Natural bundles Keywords:space-time; phase space; space-time connection; phase connection; Schouten bracket; Frölicher-Nijenhuis bracket; symplectic structure; Poisson structure; Jacobi structure × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] DOI: 10.1016/0393-0440(96)00047-2 · Zbl 0861.53026 · doi:10.1016/0393-0440(96)00047-2 [2] Janyška J., Bollettino U.M.I. 7 pp 587– [3] DOI: 10.1090/conm/288/04847 · doi:10.1090/conm/288/04847 [4] Janyška J., Arch. Math. (Brno). 42 pp 195– [5] Janyška J., Arch. Math. (Brno) 32 pp 281– [6] DOI: 10.1142/S0219887806001351 · Zbl 1095.53046 · doi:10.1142/S0219887806001351 [7] DOI: 10.1007/978-3-662-02950-3 · doi:10.1007/978-3-662-02950-3 [8] DOI: 10.1007/978-94-009-3807-6 · doi:10.1007/978-94-009-3807-6 [9] DOI: 10.1007/978-3-0348-8495-2 · doi:10.1007/978-3-0348-8495-2 [10] Vinogradov A. M., Rend. Seminari Fac. Sci. Univ. Cagliari 58 pp 301– [11] Weyl H., Gottingen Nachr. pp 99– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.