. "1"^^ . . . "C\u00EDle projektu byly spln\u011Bny. Byly z\u00EDsk\u00E1ny cenn\u00E9 p\u016Fvodn\u00ED v\u00FDsledky v geometrii vy\u0161\u0161\u00EDho \u0159\u00E1du a v oblasti geometrick\u00FDch metod ve fyzice. Z\u00E1v\u011Bre\u010Dn\u00E1 karta obsahuje \u00FApln\u00E9 \u00FAdaje o z\u00EDskan\u00FDch v\u00FDsledc\u00EDch. \u0158e\u0161en\u00ED projektu p\u0159isp\u011Blo k z\u00EDsk\u00E1n\u00ED nov\u00FDch poznatk\u016F v klasick\u00E9"@cs . . . . . "0"^^ . . "http://www.isvav.cz/projectDetail.do?rowId=GA201/99/0296"^^ . "22"^^ . . "22"^^ . . "GA201/99/0296" . "2003-04-01+02:00"^^ . . . . "Diferenci\u00E1ln\u00ED geometrie vy\u0161\u0161\u00EDho \u0159\u00E1du" . . "The project is devoted to fundamental research in differential geometry of higher order and to applications in mathematical physics. Geometric properties of various generalizations of the concept of jet, which appear in global analysis and mathematical physics, and geometric operations on them will be studied systematically. Special attention will be paid to the classification problem by using the methods from the monograph by I. Kol\u00E1o, P. W. Michor and J. Slov\u00E1k 'Natural operations in Differential Geometry', Springer-Verlag 1993, which was well accepted in mathematical public. The theory of connections on certain higher order bundles will be developed from such viewpoints. Futher, the geometry of jet bundles will be used for constructing geometricmachinery for both classical and quantum general relativity. Recent general results about parabolic geometries will be systematically applied for investigating certain second order G-structures. The technique of Weil bundles will be further developed in"@en . "Projekt se zab\u00FDv\u00E1 z\u00E1kladn\u00EDm v\u00FDzkumem v diferenci\u00E1ln\u00ED geometrii vy\u0161\u0161\u00EDho \u0159\u00E1du a jeho aplikacemi v matematick\u00E9 fyzice. Systematicky budou studov\u00E1ny geometrick\u00E9 vlastnosti r\u016Fzn\u00FDch zobecn\u011Bn\u00ED pojmu jetu a operace s nimi, kter\u00E9 se objevuj\u00ED v glob\u00E1ln\u00ED anal\u00FDze a matematick\u00E9 fyzice. Zvl\u00E1\u0161tn\u00ED pozornost bude v\u011Bnov\u00E1na klasifikaci takov\u00FDchto operac\u00ED s vyu\u017Eit\u00EDm metod z monografie I. Kol\u00E1\u0159, P. W. Michor, J. Slov\u00E1k, Natural Operations in Differential Geometry, Springer-Verlag 1993, kter\u00E1 nalezla \u0161irok\u00FD ohlas v odborn\u00E9 ve\u0159ejnosti. Z t\u011Bchto hledisek bude rozv\u00EDjena i teorie konex\u00ED na speci\u00E1ln\u00EDch prostorech vy\u0161\u0161\u00EDho \u0159\u00E1du. Geometrie jetov\u00FDch prostor\u016F bude rovn\u011B\u017E vyu\u017E\u00EDv\u00E1na p\u0159i tvorb\u011B geometrick\u00E9ho apar\u00E1tu klasick\u00E9 i kvantov\u00E9 obecn\u00E9 relativity. Ned\u00E1vno odvozen\u00E9 obecn\u00E9 v\u00FDsledko tzv. parabolick\u00FDch geometri\u00EDch budou aplikov\u00E1ny k systematick\u00E9mu studiu vybran\u00FDch G-struktur druh\u00E9ho \u0159\u00E1du. D\u00E1le bude rozpracov\u00E1v\u00E1no vyu\u017Eit\u00ED techniky Weilov\u00FDch prostor\u016F p\u0159i \u0159e\u0161en\u00ED konkr\u00E9tn\u00EDch geometrick\u00FDch probl\u00E9m\u016F." . "Neuvedeno."@en . "Differential geometry of higher order"@en . . . "1"^^ .