Project information
Prolongation of geometric structures
- Project Identification
- GA201/02/0225
- Project Period
- 1/2002 - 12/2004
- Investor / Pogramme / Project type
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Czech Science Foundation
- Standard Projects
- MU Faculty or unit
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Faculty of Science
- prof. RNDr. Ivan Kolář, DrSc.
- Cooperating Organization
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Brno University of Technology
- Responsible person prof. RNDr. Miroslav Doupovec, CSc.
The project is devoted to fundamental research in differential geometry and its applications in analytical mechanics and mathematical physics. The main subject of the research will be those prolongations of geometric structures that are based on the idea of bundle functor on a category over manifolds. The fundamental role of this concept was clarified in the monograph by I. Koláo, P.W.Michor, J. Slovák, Natural Operations in Differential Geometry, Springer-Verlag 1993, which was well accepted in mathematical public. The most important general method in this area are geometric constructions based on the notion of Weil algebra. This technique will be further developed from both theoretic and algorithmic points of view. Special attention will be paid to the torsions of connections on various natural bundles of higher order and to connections on jet spaces. In the area of applications of differential geometry in mathematical physics, the geometric methods of classical and quantum general relativi
Publications
Total number of publications: 10
2008
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Flow prolongation of some tangent valued forms
Czechoslovak Mathematical Journal, year: 2008, volume: 58, edition: 2
2006
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An outline of covariant quantum mechanics
Recent Developments in Gravitational Phzsics, year: 2006
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On the geometry of variational calculus on some functional bundles
Note di Matematica, year: 2006, volume: 2006, edition: 1
2005
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Functorial prolongations of Lie algebroids
Differential Geometry and Its Applications, Prof. Conf. Prague, August 30-September 3, 2004, year: 2005
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Higher order valued reduction theorems for classical connections
Central European Journal of Mathematics, year: 2005, volume: 3, edition: 2
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Natural connections given by general linear and classical connections
Differential Geometry and its Application, year: 2005
2004
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On the curvature of tensor product connections and covariant differentials
Supplemento di Rendiconti del Circolo Matematico di Palermo, year: 2004, volume: 72, edition: 1
2003
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On the flow prolongation of vector fields
Proceedings of Geometrical Seminar, Kazaň, year: 2003
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On the torsion of linear higher order connections
Central European Journal of Mathematics, year: 2003, volume: 3, edition: 3
2002
-
Covariant Schroedinger operator
J. Phys. A: Math. Gen., year: 2002, volume: 35, edition: 40