Project detail

Global analysis and the geometry of fibred spaces

Duration: 01.01.2009 — 31.12.2013

Funding resources

Czech Science Foundation - Standardní projekty

- whole funder (2009-01-01 - 2013-12-31)

On the project

Projekt je zaměřen na výzkum v oblasti globální analýzy a geometrie fibrovaných prostorů, především na tato témata:- variační analýza a geometrie Lagrangeových struktur na varietách,- diferenciální rovnice na prostorech jetů, diferenciální vazby,- diferenciální geometrie fibrovaných prostorů a její aplikace,- přirozené a kalibračně-přirozené bandly a operátory, přirozené variační principy, dierenciální invarianty,- geometrické a variační struktury v mechanice vyššího řádu a teorii pole.Výzkumný tým je tvořen mezinárodně uznávanými odborníky i mladými vědci a doktorandy. Jeho členem je také vynikající zahraniční odborník prof. D. Saunders (Velká Británie). Důležitým rysem projektu je i příspěvek k integraci dosavadní mezinárodní spolupráce při řešení výzkumné problematiky.

Description in English
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.

Keywords
fibrované prostory, bandly, Lagrangeovy struktury, Hamiltonovy struktury, variační analýza

Key words in English
fibred spaces; Weil bundles; Lagrangian structures; Hamiltonian structures; variational sequences

Mark

GA201/09/0981

Default language

Czech

People responsible

Doupovec Miroslav, prof. RNDr., CSc., dr. h. c. - fellow researcher
Rossi Olga, prof. RNDr., DrSc. - principal person responsible

Units

Institute of Mathematics
- co-beneficiary (2009-01-01 - 2013-12-31)

Results

DOUPOVEC, M.; MIKULSKI, W. On iteration of higher order jets and prolongation of connections. Annales Polon.Math., 2011, vol. 100, no. 1, p. 55-75. ISSN: 0066-2216.
Detail

DOUPOVEC, M.; KUREŠ, M. Some geometric constructions on Frobenius Weil bundles. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2014, vol. 35, no. S, p. 143-149. ISSN: 0926-2245.
Detail

KUREŠ, M. From optimal control problems to foliations, some kinds of multifoliations and relations to generalised jets. Journal of Quality Measurement and Analysis, 2010, vol. 6, no. 2, p. 19-32. ISSN: 1823-5670.
Detail

KUREŠ, M. Fixed point subalgebras of Weil algebras: from geometric to algebraic questions. In Complex and Differential Geometry. Springer Proceedings in Mathematics. Berlin Heidelberg: Springer, 2011. p. 183-192. ISBN: 978-3-642-20299-5.
Detail

KUREŠ, M. On some directions in the development of jet calculus. Banach Center Publications, 2011, vol. 93, no. 1, p. 251-260. ISSN: 0137-6934.
Detail

HRDINA, J. Geometric properties of Frobenius algebras. Journal of Physics: Conference Series, 2012, vol. 2012, no. 1, p. 1-5. ISSN: 1742-6588.
Detail

KUREŠ, M. Looking at osculating bundles through the semiholonomity equalizations. Advances and Applications in Mathematical Sciences, 2011, vol. 10, no. 7, p. 1-8. ISSN: 0974-6803.
Detail

KUREŠ, M. Weil algebras associated to functors of third order semiholonomic velocities. Mathematical Journal of Okayama University, 2014, vol. 56, no. 1, p. 117-127. ISSN: 0030-1566.
Detail

HRDINA, J.; VAŠÍK, P. Generalized geodesics on almost Cliffordian geometries. Balkan Journal of Geometry and Its Applications, 2012, vol. 17 (2012), no. 1, p. 41-48. ISSN: 1224-2780.
Detail

KUREŠ, M. Finite dimensional factor algebras of F2[X1,...,Xn] and their fixed point subalgebras. Open Journal of Applied Sciences, 2012, vol. 2, no. Suppl., p. 212-214. ISSN: 2165-3917.
Detail

HRDINA, J.; VAŠÍK, P. Semiholonomic second order connections associated to materia bodies. Journal of Applied Mathematics, 2013, vol. 2013, no. 1, p. 1-5. ISSN: 1110-757X.
Detail

KUREŠ, M. Jet theory in microstructures. Key Engineering Materials (print), 2014, vol. 592-593, no. 1, p. 125-128. ISSN: 1013-9826.
Detail

KUREŠ, M. Lagrangians on iterated tangent bundles and the Hamiltonization. Miskolc Mathematical Notes, 2013, vol. 14, no. 2, p. 525-538. ISSN: 1787-2405.
Detail

KUREŠ, M. A note to geometry of Cosserat media and deformation bundles. Transylvanian Journal of Mathematics and Mechanics, 2014, vol. 6, no. 1, p. 39-43. ISSN: 2067-239X.
Detail

DOUPOVEC, M.; MIKULSKI, W. On symmetrization of higher order jets. Miskolc Mathematical Notes, 2013, vol. 14, no. 2, p. 495-502. ISSN: 1787-2405.
Detail

DOUPOVEC, M.; KOLÁŘ, I.; MIKULSKI, W. On the jets of foliation respecting maps. Czechoslovak Mathematical Journal, 2010, vol. 60, no. 4, p. 951-960. ISSN: 0011-4642.
Detail

Responsibility: Rossi Olga, prof. RNDr., DrSc.