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Some gauge-natural operators on linear connections. (English) Zbl 0722.53020
The authors determine all geometrical operators transforming a linear connection on a vector bundle \(E\to M\) and a classical linear connection on the base manifold M into a classical linear connection on the total space E. The result is a 15-parameter family which is explicitly determined and interpreted geometrically.
Reviewer: J.Gancarzewicz

53C05 Connections, general theory
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[1] Eck, D. J.: Gauge-natural bundles and generalized gauge theories. Mem. Amer. Math. Soc.33, No. 247 (1981). · Zbl 0493.53052
[2] Epstein, D. B. A., Thurston, W. P.: Transformation groups and natural bundles. Proc. London Math. Soc. (3)38, 219–236 (1979). · Zbl 0409.58001 · doi:10.1112/plms/s3-38.2.219
[3] Gancarzewicz, J.: Horizontal lifts of linear connections to the natural vector bundle. In: Proc. Inter. Coll. Diff. Geometry, Santiago de Compostela (Spain). Research Notes in Math. 121, pp. 318–319. Boston: Pitman. 1985. · Zbl 0646.53028
[4] Kolář, I.: Some natural operators in differential geometry. In: Proc. Conf. Diff. Geometry and Its Appl., August 24–30, 1986, pp. 91–110. Eds.D. Krupka andA. Švec, J. E. Purkyně University, Brno 1987.
[5] Kolář, I.: Some gauge-natural operators on connections. To appear. · Zbl 0806.53025
[6] Kolář, I., Vosmanská, G.: Natural transformations of higher order tangent bundles and jet spaces. Čas. pěst. mat.114, 181–186 (1989). · Zbl 0678.58002
[7] Kolář, I., Michor, P. W., Slovák, J.: Natural operations in differential geometry. To appear. · Zbl 0782.53013
[8] Palais, R. S., Terng, C.-L.: Natural bundles have finite order. Topology16, 271–277 (1977). · Zbl 0359.58004 · doi:10.1016/0040-9383(77)90008-8
[9] Slovák, J.: On the finite order of some operators. In: Proc. Conf. Diff. Geometry and Its Appl. (Communications) August 24–30, 1986, Brno, pp. 283–294.
[10] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles. New York: Marcel Dekker. 1973. · Zbl 0262.53024
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