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Title: Natural differential operators between some natural bundles (English)
Author: Mikulski, W. M.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 118
Issue: 2
Year: 1993
Pages: 153-161
Summary lang: English
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Category: math
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Summary: Let $F$ and $G$ be two natural bundles over $n$-manifolds. We prove that if $F$ is of type (I) and $G$ is of type (II), then any natural differential operator of $F$ into $G$ is of order 0. We give examples of natural bundles of type (I) or of type (II). As an application of the main theorem we determine all natural differential operators between some natural bundles. (English)
Keyword: natural bundles
Keyword: natural differential operators
MSC: 53A55
MSC: 58A20
idZBL: Zbl 0777.58004
idMR: MR1223480
DOI: 10.21136/MB.1993.126052
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Date available: 2009-09-24T20:58:07Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/126052
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Reference: [1] J. Dębecki: Natural transformations of afinors into functions and afìnors.Supplemento ai Rendiconti del Circolo Matematico di Palermo (1991), in press.
Reference: [2] D. B. A. Epstein: Natural tensors on Riemmannian manifolds.Ј. Differential Geometry, 631-645. MR 0415531
Reference: [3] D. B. A. Epstein W.P. Thurston: Transformation groups and natural bundles.Proc. London Math. Soc. (3) 38 (1979), 219-236. MR 0531161
Reference: [4] J. Gancarzewicz: Differential Geometry.B.M.64, 1987. (In Polish.) MR 0944676
Reference: [5] J. Gancarzewicz: Liftings of functions and vector fields to natural bundles.Dissertationes Mathematicae, Warszawa (1982). Zbl 0503.53050, MR 0663216
Reference: [6] T. Klein: Connection on higher order tangent bundles.Čas. Pӗst. Mat. 106 (1981), 414-424. MR 0637822
Reference: [7] I. Kolář: Functorial prolongations of Lie groups and their actions.Čas. Pěst. Mat. 108 (1983), 289-294. MR 0716414
Reference: [8] I. Kolář J. Slovák: On the geometric functors on manifolds.Suplemento ai Rendiconti del Circolo Matematico di Palermo (1988), 223-233. MR 1009575
Reference: [9] W. M. Mikulski: Continuity of liftings.Čas. Pěst. Mat. 113 (4) (1988), 359-362. Zbl 0677.58006, MR 0981877
Reference: [10] A. Morimoto: Prolongations of connections to bundles of infinitely near points.Ј. Differential Geometry 11 (1976), 479-498. MR 0445422, 10.4310/jdg/1214433720
Reference: [11] A. Nijenhuis: Natural bundles and their general properties.Differential Geometry, Kinokuniya, Тokio (1972), 317-343. Zbl 0246.53018, MR 0380862
Reference: [12] R. S. Palais C. L. Terng: Natural bundles have finite order.Тopology 16 (1977), 271-277. MR 0467787
Reference: [13] J. Slovák: On the finite ordeг of some operators.Proc. of the Conf., Brno, 1986.
Reference: [14] A. Zajtz: Foundation of differential geometry on natural bundles.Caracas, 1984, preprint.
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