Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
spacetime; spacetime connection; Schouten bracket; Frölicher–Nijenhuis bracket; symplectic structure; Poisson structure
spacetime; spacetime connection; Schouten bracket; Frölicher–Nijenhuis bracket; symplectic structure; Poisson structure
Summary:
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.
References:
[1] Janyška J.: Remarks on symplectic and contact 2–forms in relativistic theories. Boll. Un. Mat. Ital. B (7) 9 (1995), 587–616. MR 1351076 | Zbl 0857.53027
[2] Janyška J.: Natural symplectic structures on the tangent bundle of a space–time. The Proceedings of the Winter School Geometry and Topology (Srní, 1995), Rend. Circ. Mat. Palermo (2) Suppl. 43 (1996), 153–162. MR 1463517
[3] Janyška J., Modugno M.: Classical particle phase space in general relativity. Differential Geometry and Applications, Proc. Conf., Aug. 28 – Sept. 1, 1995, Brno, Czech Republic, Masaryk University, Brno 1996, 573–602. MR 1406377
[4] Janyška J., Modugno M.: On quantum vector fields in general relativistic quantum mechanics. in: Proc. 3rd Internat. Workshop Differential Geom. Appl., Sibiu (Romania) 1997, General Mathematics 5 (1997), 199–217. MR 1723610 | Zbl 0956.53054
[5] Janyška J.: Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold. Contemporary Mathematics 288 (2001), Global Differential Geom.: The Math. Legacy of Alfred Gray, eds. M. Fernándes and J. A. Wolf, 343–347. MR 1871030 | Zbl 1013.53053
[6] Janyška J.: Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold. Arch. Math. (Brno) 37 (2001), 143–160. MR 1838411 | Zbl 1090.58007
[7] Krupka D., Janyška J.: Lectures on Differential Invariants. Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., 1990. MR 1108622
[8] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry. Springer–Verlag 1993. MR 1202431
[9] Libermann P., Marle, Ch. M.: Symplectic Geometry and Analytical Mechanics. Reidel Publ., Dordrecht 1987. MR 0882548 | Zbl 0643.53002
[10] Nijenhuis A.: Natural bundles and their general properties. Differential Geom., in honour of K. Yano, Kinokuniya, Tokyo 1972, 317–334. MR 0380862 | Zbl 0246.53018
[11] Vaisman I.: Lectures on the Geometry of Poisson Manifolds. Birkhäuser Verlag 1994. MR 1269545 | Zbl 0810.53019
Search
Partner of
