Project information
Global analysis and the geometry of fibred spaces
- Project Identification
- GA201/09/0981
- Project Period
- 1/2009 - 12/2013
- Investor / Pogramme / Project type
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Czech Science Foundation
- Standard Projects
- MU Faculty or unit
- Faculty of Science
- Keywords
- fibred spaces; Weil bundles; Lagrangian structures; Hamiltonian structures; variational sequences an
- Cooperating Organization
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Palacký University, Olomouc
- Responsible person prof. RNDr. Olga Rossi, DrSc.
- Responsible person prof. RNDr. Miroslav Doupovec, CSc.
This project covers the following research topics in global analysis and the geometry of fibred spaces:- variational analysis and the geometry of Lagrange structures on manifolds,- differential equations on jet bundles, including differential constraints,- differential geometry of fibred spaces and its applications,- natural and gauge-natural bundles and operators, natural variational principles, differential invariants,- geometric and variational structures in higher order mechanics and field theory.The research team involved in this project includes recognized leading experts in the fields above, as well as young researchers and PhD students. The aim of the project is to contribute to developments in the broad area of global analysis, differential geometry and the applications of geometric and variational methods in mathematical physics. One of the aims is also to integrate top research in the Czech Republic in global analysis and the geometry of fibred spaces. Main outputs will be
Publications
Total number of publications: 38
2014
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Classification of Principal Connections on (W)over-tilde(2)PE
Algebra, Geometry and Mathematical Physics (AGMP), year: 2014
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Natural transformations of connections on the first principal prolongation
Archivum Mathematicum, year: 2014, volume: 50, edition: 1, DOI
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On the geometry of Weil bundles
Differential Geometry and Its Applications, year: 2014, volume: 35, edition: September, DOI
2013
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Nonholonomic mechanics: A practical application of the geometrical theory on fibred manifolds to a planimeter motion
International Journal of Non-Linear Mechanics, year: 2013, volume: 50, edition: April 2013, DOI
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On the functorial prolongations of fiber bundles
MISKOLC MATHEMATICAL NOTES, year: 2013, volume: 14, edition: 2
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On the natural transformations of Weil bundles
Archivum Mathematicum (Brno), year: 2013
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The inverse variational problem in nonholonomic mechanics
Year: 2013, type: Appeared in Conference without Proceedings
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The nonholonomic inverse variational problem in mechanics
Year: 2013, type: Appeared in Conference without Proceedings
2012
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Cartan-Lepage forms in geometric mechanics
International Journal of Non-Linear Mechanics, year: 2012, volume: 47, edition: 10, DOI
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Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case
Archivum Mathematicum, year: 2012, volume: 48, edition: 1, DOI