| Title:
|
Geometric structures on the tangent bundle of the Einstein spacetime (English) |
| Author:
|
Janyška, Josef |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
195-203 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
spacetime |
| Keyword:
|
spacetime connection |
| Keyword:
|
Schouten bracket |
| Keyword:
|
Frölicher–Nijenhuis bracket |
| Keyword:
|
symplectic structure |
| Keyword:
|
Poisson structure |
| MSC:
|
53B15 |
| MSC:
|
53B30 |
| MSC:
|
53D05 |
| MSC:
|
53D17 |
| idZBL:
|
Zbl 1164.53318 |
| idMR:
|
MR2240357 |
| . |
| Date available:
|
2008-06-06T22:47:59Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107996 |
| . |
| Reference:
|
[1] Janyška J.: Remarks on symplectic and contact 2–forms in relativistic theories.Boll. Un. Mat. Ital. B (7) 9 (1995), 587–616. Zbl 0857.53027, MR 1351076 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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. Zbl 0956.53054, MR 1723610 |
| Reference:
|
[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. Zbl 1013.53053, MR 1871030 |
| Reference:
|
[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. Zbl 1090.58007, MR 1838411 |
| Reference:
|
[7] Krupka D., Janyška J.: Lectures on Differential Invariants.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., 1990. MR 1108622 |
| Reference:
|
[8] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry.Springer–Verlag 1993. MR 1202431 |
| Reference:
|
[9] Libermann P., Marle, Ch. M.: Symplectic Geometry and Analytical Mechanics.Reidel Publ., Dordrecht 1987. Zbl 0643.53002, MR 0882548 |
| Reference:
|
[10] Nijenhuis A.: Natural bundles and their general properties.Differential Geom., in honour of K. Yano, Kinokuniya, Tokyo 1972, 317–334. Zbl 0246.53018, MR 0380862 |
| Reference:
|
[11] Vaisman I.: Lectures on the Geometry of Poisson Manifolds.Birkhäuser Verlag 1994. Zbl 0810.53019, MR 1269545 |
| . |
