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Project information
Prolongation of geometric structures

Investor logo
Project Identification
GA201/02/0225
Project Period
1/2002 - 12/2004
Investor / Pogramme / Project type
Czech Science Foundation
  • Standard Projects
MU Faculty or unit
Faculty of Science
  • prof. RNDr. Ivan Kolář, DrSc.
Cooperating Organization
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

2006

2005

2004

2003

2002

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