Project detail

Geometry of liber bundles

Duration: 01.01.1996 — 31.12.1998

Funding resources

Czech Science Foundation - Standardní projekty

- whole funder (1996-01-01 - 1998-12-31)

On the project

Projekt se zabývá základním výzkumem v diferenciální geometrii fibrovaných prostorů a jeho aplikacemi v matematické fyzice. Hlavním metodickým východiskem bude monografie I.Kolář, P.W.Michor, J.Slovák, Natural Operations in Differential Geometry, Springe r-Verlag 1993. V souvislosti s novými podněty z matematické fyziky bude vytvořena knižní monografie o geometrii fibrovaných prostředků hladkých zobrazení, která vyjasní také úlohu Weilových prostorů v této oblasti. S využitím representačních technik budo u klasifikovány přirozené operátory na některých G-strukturách a budou studovány jejich prolongace. Teorie přirozených operací bude dále rozvíjena v souvislosti se studiem konkrétních problémů v diferenciální geometrii vyššího řádu. Zvláštní pozornost bu de věnována obecným konexím na fibrovaných prostorech s dodatečnou geometrickou strukturou v souvislosti s jejich vztahy k rovnicím analytické mechaniky.

Description in English
The project is devoted to fundamental research in geometry of fiber bundles and to applications in mathematical physics. The research methods will be mostly based on a monograph by I. Kolar, P. W. Michor and J. Slovak 'Natural Operations in DifferentialGeometry', Springer-Verlag 1993. Taking into consideration new problems in mathematical physics, a book on the geometry of bundles of smooth maps will be written. Lthe book will also clarify the role of Weil bundles in this area. Natural operators on some G-structures will be classified by using representation techniques and prolongations of such structures will be studied. Further development of the theory of natural operators will be related with investigating of concrete problems in higher order geometry. Special attention will be paid to general connections in fibered manifolds with additional structures and to their relations to the equations of analytical mechanics.

Mark

GA201/96/0079

Default language

Czech

People responsible

Doupovec Miroslav, prof. RNDr., CSc., dr. h. c. - fellow researcher

Units

Institute of Mathematics
- beneficiary (1996-01-01 - 1998-12-31)
Faculty of Mechanical Engineering
- co-beneficiary (1996-01-01 - 1998-12-31)

Results

KUREŠ, M. In Differential geometry and Applications - Satellite Conferenc. Brno, ČR: MU Brno, 1899. p. 239 ( p.)ISBN: 80-210-209.
Detail

DOUPOVEC, M. On the symplectic structure of some natural bundles. In Differential Geometry and Its Applications, Proceedings. Satellite Conference of ICM in Berlin, Aug. 10-14, 1988, Brno. Brno: Masaryk University, Brno, 1999. p. 223 ( p.)ISBN: 80-210-2097-0.
Detail

TOMÁŠ, J. Natural T-functions on the cotangent bundle of some Weil bundles. In Differential Geometry and Its Applications, Proceedings of the Satelite Conference of ICM in Berlin, Brno, August 1998. Brno: 1999. p. 293-302 ( p.)ISBN: 80-210-2097-0.
Detail

DOUPOVEC, M., VONDRA, A. Connection, jet prolongation, natural operator, integrability. Supplemento ai Rendiconti del Circolo Matematico di Palermo, 1996, vol. 39, no. 0, p. 73 ( p.)ISSN: 0009-725X.
Detail

DOUPOVEC, M., KUREK, J. Natural operations of Hamiltonian type on the cotangent bundle. Supplemento ai Rendiconti del Circolo Matematico di Palermo, 1997, vol. 46, no. Serie II, p. 81 ( p.)ISSN: 0009-725X.
Detail

DOUPOVEC, M., KUREK, J. Liftings of 1-forms to some non product preserving bundles. Supplemento ai Rendiconti del Circolo Matematico di Palermo, 1998, vol. 54, no. Serie II, p. 26 ( p.)ISSN: 0009-725X.
Detail

DOUPOVEC, M., VONDRA, A. Invariant subspaces in higher order jet prolongations of a fibred manifold. Czechoslovak Mathematical Journal, 2000, vol. 50, no. 125, p. 209 ( p.)ISSN: 0011-4642.
Detail

KUREŠ, M. Torsions of connections on tangent bundles of higher order. 1998, vol. 54, no. II, p. 65 ( p.)
Detail

KUREŠ, M. Some properties of connections on iterated tangent bundles. Archives of Mechanics, 1998, vol. 50, no. 3, p. 459 ( p.)ISSN: 0373-2029.
Detail

DOUPOVEC, M., KOLÁŘ, I. On the jets of fibered manifold morphisms. Cahiers de Topologie et Geometrie Differentielle Categoriques, 1999, vol. XL, no. 1, p. 21 ( p.)ISSN: 0008-0004.
Detail

TOMÁŠ, J. On quasijet bundles. Supplemento ai Rendiconti del Circolo Matematico di Palermo, 2000, no. 63, p. 187-196 ( p.)ISSN: 0009-725X.
Detail

TOMÁŠ, J.; KOLÁŘ, I. Gauge-natural transformations of some cotangent bundles. 1997, no. 5, p. 3 ( p.)ISSN: 80-88825-111-1.
Detail

TOMÁŠ, J. Natural operators on vector fields on the cotangent bundle of the bundles of (k,r)-velocities. Supplemento ai Rendiconti del Circolo Matematico di Palermo, 1998, vol. 1997, no. 54, p. 113 ( p.)ISSN: 0009-725X.
Detail

TOMÁŠ, J. Natural T-functions on the cotangent bundle of a Weil bundle. Czechoslovak Mathematical Journal, 2004, vol. 54, no. 129, p. 868-882. ISSN: 0011-4642.
Detail

KUREŠ, M. Affinors and connections in higher order geometry. In Differential Geometry and Applications. Brno: Ed.: I. Kolář,..., 1999. p. 239 ( p.)ISBN: 80-210-2097-0.
Detail

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