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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
0. Introduction...................................................................................................5
1. Natural bundles...........................................................................................10
2. Liftings of functions.....................................................................................15
3. Liftings of functions to the r-frame bundle...................................................22
4. A space of liftings of functions.....................................................................26
5. Quasi-liftings and liftings of vector fields to a natural bundle.......................32
6. Liftings of vector fields to tangent bundles of $p^r$-velocities.....................39
7. Decomposition theorem...............................................................................44
8. Liftings of vector fields to some associated fibre bundles............................49
9. Final remarks...............................................................................................53
References......................................................................................................54
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
212
Liczba stron
55
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXII
Daty
wydano
1983
Twórcy
autor
Bibliografia
- [1] J. Aczél und S. Gołąb, Funktionalgleinchungen der Theorie der Geometrischen Objekte, PWN, Warszawa 1960.
- [2] D. Cerveau, Distributions involutives singulières, Ann. Inst. Fourier, Grenoble, 29 (1979), pp. 261- 294.
- [3] C. Ehresmann, Les prolongements d'un espace fibré différentiable, C. R. Acad. Sci. Paris 240 (1955), pp. 1755-1757.
- [4] D. B. A. Epstein and W. P. Thurston, Transformation groups and natural bundles, Proc. London Math. Soc. 38 (1979), pp. 219-237.
- [5] J. Gancarzewicz, Local triviality of bundles of geometric objects, Zeszyty Naukowe UJ 23 (1981) (in press).
- [6] J. Gancarzewicz, Complete lifts of tensor fields of type (1, k) to natural bundles, Zeszyty Naukowe UJ 23 (1981) (in press).
- [7] J. Gancarzewicz, Liftings of functions and vector fields to natural bundles. Preprint PAN no 207, Warsaw, March 1980.
- [8] V. Guillimin and S. Stenberg, Deformation theory of pseudogroup structures, Mem. Amer. Math. Soc. 64 (1966).
- [9] S. Kobayashi and K. Nomizu, Foundations of differential geometry I, New York 1963.
- [10] I. Kolar, Structure morphisms of prolongation functors, Math. Slovaca 30 (1980), pp. 83-93.
- [11] I. Kolar, Lecture in Banach Centre, Warsaw, November 1979.
- [12] D. Krupka, Reducibility theorems for differentiable liftings in fibre bundles, Arch. Math. Scripta Fac. Sc. Nat. Ujep Brunensis 15 (1979), pp. 93-106.
- [13] K.-P. Mok, Complete lifts of tensor fields and connections from a manifold to the linear frame bundle. Proc. London Math. Soc. 38 (1979), pp. 72-88.
- [14] P. Molino, Théorie des G-structures. Le problème d'equivalence, Lect. Notes in Math, no 588, Springer-Verlag, 1977.
- [15] A. Morimoto, Prolongations of geometric structures, Lect. Notes, Math. Inst. Nagoya Univ. 1969.
- [16] A. Morimoto, Prolongations of G-structures to tangent bundles, Nagoya Math. J. 32 (1968), pp. 67-108.
- [17] A. Morimoto, Prolongations of G-structures to tangent bundles of higher order, Nagoya Math. J. 38 (1970), pp. 153-179.
- [18] A. Morimoto, Liftings of some types of tensor fields and connections to tangent bundles of $p^r$-velocities, Nagoya Math. J. 40 (1970), pp. 13-31.
- [19] A. Morimoto, Prolongations of connections to tangential fibre bundles of higher order, Nagoya Math. J. 40 (1970), pp. 85-97.
- [20] A. Morimoto, Liftings of tensor fields and connections to tangent bundles of higher order, Nagoya Math. J. 40 (1970), pp. 99-120.
- [21] A. Morimoto, Prolongations of connections to bundles of infinitely near points, J. Diff. Geom. 11 (1976), pp. 476-498.
- [22] A. Nijenhuis, Geometric aspects of formal differential operations on tensor fields, Proc. Int. Congr. Math, Cambrige Univ. Press (I960), pp. 14-21.
- [23] A. Nijenhuis, Natural bundles and their general properties, Diff. Geom. in honor of K. Yano, Kinokuniya, Tokio 1972, pp. 317-334.
- [24] R. S. Palais and C.-L. Terng, Natural bundles have a finite order. Topology 16 (1978), pp. 271-277.
- [25] S. E. Salvioli, Theory of geometric object, J. Diff. Geom. 7 (1972), pp. 257-278.
- [26] H. I. Susman, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), pp. 173-188.
- [27] C.-L. Terng, Natural vector bundles and natural differential operators, Ann. Math. J. 100 (1978), pp. 775-828.
- [28] K. Yano and S. Ishihara, Differential geometry in tangent bundles, Kodai Math. Sem. Rep. 18 (1966), pp. 271-292.
- [29] K. Yano and S. Ishihara, Differential geometry of tangent bundles of order 2, Kodai Math. Sem. Rep. 20 (1968), pp. 318-354.
- [30] K. Yano and S. Ishihara, Tangent and cotangent bundles, Marcel Dekker, INC., New York 1973.
- [31] K. Yano and S. Kobayashi, Prolongations of tensor fields and connections to tangent bundle. (I) General theory, (II) Affine automorphism, (III) Holonomy groups, J. Math. Soc. Japan 18 (1966), pp. 194-210; 18 (1966), pp. 236-246; 19 (1967), pp. 486-488.
- [32] K. Yano and E. Patterson, Vertical and complete lifts from a manifold to its contangent bundle, J. Math. Soc. Japan 19 (1967), pp. 91-113.
- [33] C. Yuen, Sur les relèvements des dérivations aux espaces tangents. Relèvements verticaux et relèvements complets, C. R. Acad. Sci. Paris 282 (1976), pp. 371-373.
- [34] C. Yuen, Relèvements de dérivations aux fibres tangents d'ordre 2, C. R. Acad. Sci. Paris 282 (1976), pp. 703-706.
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