Project details


Geometric structures on fibered manifolds

Project Identification:GA201/05/0523
Project Period:1/2005 - 12/2007
Investor:link to a new windowCzech Science Foundation
Programme / Project Type:Standard Projects -
MU Faculty/Unit:
Faculty of Science
MU Investigator:Prof. RNDr. Miroslav Doupovec, CSc.
Project Team Member:Prof. RNDr. Josef Janyška, DSc.
Field:BA - General mathematics (B - Physics and mathematics)
Keywords:Weil bundle, natural operator, gauge natural operator

The project deals with the fundamental research in differential geometry and its applications in analytical mechanics and mathematical physics. The principal attention will be paid to the Weil algebra technique in differential geometry of fiberedmanifold s. Further, the following topics will be dealt with: the objects of Weilian type on certain functional bundles, relations to the geometry of variational calculus, natural bundles over fibered manifolds, prolongation of connections, fiber productpreservin g bundle functors of the jet type, exchange natural transformations of cotangent and Weil functors. Further types of natural differential operators will be studied. In the area of applications of differential geometry in mathematical physics,the geometri c problems related with covariant classical and quantum mechanics will be studied. In particular, concrete natural operators in Galilei and Einstein quantum mechanics will be investigated and the gauge version of the reduction method for