Geometric structures on the tangent bundle of the Einstein spacetime
Archivum Mathematicum (2006)
- Volume: 042, Issue: 2, page 195-203
- ISSN: 0044-8753
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topJanyška, Josef. "Geometric structures on the tangent bundle of the Einstein spacetime." Archivum Mathematicum 042.2 (2006): 195-203. <http://eudml.org/doc/249810>.
@article{Janyška2006,
abstract = {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.},
author = {Janyška, Josef},
journal = {Archivum Mathematicum},
keywords = {spacetime; spacetime connection; Schouten bracket; Frölicher–Nijenhuis bracket; symplectic structure; Poisson structure; spacetime; spacetime connection; Schouten bracket; Frölicher-Nijenhuis bracket; symplectic structure},
language = {eng},
number = {2},
pages = {195-203},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Geometric structures on the tangent bundle of the Einstein spacetime},
url = {http://eudml.org/doc/249810},
volume = {042},
year = {2006},
}
TY - JOUR
AU - Janyška, Josef
TI - Geometric structures on the tangent bundle of the Einstein spacetime
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 2
SP - 195
EP - 203
AB - 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.
LA - eng
KW - spacetime; spacetime connection; Schouten bracket; Frölicher–Nijenhuis bracket; symplectic structure; Poisson structure; spacetime; spacetime connection; Schouten bracket; Frölicher-Nijenhuis bracket; symplectic structure
UR - http://eudml.org/doc/249810
ER -
References
top- Janyška J., Remarks on symplectic and contact 2–forms in relativistic theories, Boll. Un. Mat. Ital. B (7) 9 (1995), 587–616. (1995) Zbl0857.53027MR1351076
- 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. (1995) MR1463517
- 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. (1995) MR1406377
- 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. (1997) Zbl0956.53054MR1723610
- 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. Zbl1013.53053MR1871030
- 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. Zbl1090.58007MR1838411
- Krupka D., Janyška J., Lectures on Differential Invariants, Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., 1990. (1990) MR1108622
- Kolář I., Michor P. W., Slovák J., Natural Operations in Differential Geometry, Springer–Verlag 1993. (1993) MR1202431
- Libermann P., Marle, Ch. M., Symplectic Geometry and Analytical Mechanics, Reidel Publ., Dordrecht 1987. (1987) Zbl0643.53002MR0882548
- Nijenhuis A., Natural bundles and their general properties, Differential Geom., in honour of K. Yano, Kinokuniya, Tokyo 1972, 317–334. (1972) Zbl0246.53018MR0380862
- Vaisman I., Lectures on the Geometry of Poisson Manifolds, Birkhäuser Verlag 1994. (1994) Zbl0810.53019MR1269545
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