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Project detail
Duration: 01.01.2005 — 31.12.2007
Funding resources
Czech Science Foundation - Standardní projekty
- whole funder (2005-01-01 - 2007-12-31)
On the project
Projekt se zabývá základním výzkumem v diferenciální geometrii a jeho aplikacemi v analytické mechanice a matematické fyzice. Hlavní pozornost bude věnována technice Weilových algeber v diferenciální geometrii fibrovaných variet. Předmětem výzkumu budedá le následující problematika: objekty Weilovského typu na některých funkcionálních bandlech, souvislosti s geometrií variačního počtu, přirozené bandly na fibrovaných varietách, prodlužování konexí, bandlové funktory jetového typu zachovávajícífibrované s oučiny, výměnné přirozené transformace kotečných a Weilových funktorů. Budou se dále studovat další typy přirozených operátorů. V oblasti aplikací diferenciální geometrie v matematické fyzice budou studovány geometrické problémy související skovariantní klasickou a kvantovou mechanikou
Description in EnglishThe 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 fibered manifolds. 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 product preserving 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 geometric 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
Mark
GA201/05/0523
Default language
Czech
People responsible
Janyška Josef, doc. RNDr., CSc. - fellow researcherDoupovec Miroslav, prof. RNDr., CSc., dr. h. c. - principal person responsible
Units
Institute of Mathematics- (2005-01-01 - 2007-12-31)
Results
DOUPOVEC, M.; MIKULSKI, W. Prolongation of connections to vertical bundles. In Differential Geometry and its Applications. Praha: 2005. p. 217-227. ISBN: 80-86732-63-0.Detail
TOMÁŠ, J.; MIKULSKI, W. Reduction for natural operators on projectable connections. Demonstratio Mathematicae, 2009, vol. 42, no. 2, p. 435-439. ISSN: 0420-1213.Detail
DOUPOVEC, M.; MIKULSKI, W. On involutions of iterated bundle functors. Colloquium Mathematicum, 2006, vol. 106, no. 1, p. 135-145. ISSN: 0010-1354.Detail
DOUPOVEC, M.; MIKULSKI, W. Non-existence of exchange transformations of iterated jet functors. Banach Center Publications, 2007, vol. 76, no. 1, p. 497-504. ISSN: 0137-6934.Detail
TOMÁŠ, J. Non-holonomic (r,s,q)-jets. Czechoslovak Mathematical Journal, 2006, vol. 56, no. 131, p. 1131-1145. ISSN: 0011-4642.Detail
KUREŠ, M. Local approach to higher order contact elements. Reports on Mathematical Physics, 2006, vol. 58, no. 2, p. 393-409. ISSN: 0034-4877.Detail
TOMÁŠ, J.; MIKULSKI, W. Bundles of contact elements on fibered fibered manifolds. Demonstratio Mathematicae, 2007, vol. 40, no. 2, p. 485-493. ISSN: 0420-1213.Detail
DOUPOVEC, M.; MIKULSKI, W. Gauge natural constructions on higher order principal prolongations. Annales Polon.Math., 2007, vol. 92, no. 1, p. 87-97. ISSN: 0066-2216.Detail
VAŠÍK, P. On the Ehresmann Prolongation. Annales Universitatis Mariae Curie Sklodowska, 2007, vol. LXI, no. Sectio A, p. 145-153. ISSN: 0365-1029.Detail
DOUPOVEC, M.; MIKULSKI, W. Higher order jet involution. Czechoslovak Mathematical Journal, 2007, vol. 57, no. 132, p. 933-945. ISSN: 0011-4642.Detail
KUREŠ, M. On the connectedness of jet groups and groups of automorphisms of Weil algebras. Journal of Applied Mathematics, Statistics and Informatics., 2007, vol. 3, no. 2, p. 209-214. ISSN: 1336-9180.Detail
DOUPOVEC, M.; MIKULSKI, W. Some geometric constructions of second order connections. Annales Universitatis Mariae Curie Sklodowska, 2007, vol. 61, no. 1, p. 15-22. ISSN: 0365-1029.Detail
DOUPOVEC, M.; MIKULSKI, W. Holonomic extension of connections and symmetrization of jets. Reports on Mathematical Physics, 2007, vol. 60, no. 2, p. 299-316. ISSN: 0034-4877.Detail
KUREŠ, M. Weil modules and gauge bundles. Acta Mathematica Sinica, 2006, vol. 22, no. 1, p. 271-278. ISSN: 1439-8516.Detail
DOUPOVEC, M. On the underlying lower order bundle functors. Czechoslovak Mathematical Journal, 2005, vol. 55, no. 130, p. 901-916. ISSN: 0011-4642.Detail
VAŠÍK, P. Connections on higher order principal prolongations. Supplemento ai Rendiconti del Circolo Matematico di Palermo, 2006, vol. 79, no. Suppl. 79, p. 183-192. ISSN: 0009-725X.Detail