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On Weil bundles of the first order. (English) Zbl 1370.58001

The paper is devoted to some geometric operations on Weil bundles. The author first describes lifts of functions and vector fields to Weil bundles. Then, he defines actions of the automorphisms group of the Whittney sum of algebras of dual numbers on a Weil bundle.

MSC:

58A20 Jets in global analysis
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References:

[1] Vishnevsky, V. V., Shirokov, A. P., Shurygin, V. V.: Spaces over Algebras. Kazan University Press, Kazan’, 1984.
[2] Kolář, I., Michor, P., Slovák, J.: Natural Operation in Differential Geometry. Springer-Verlag, Berlin, 1993. · Zbl 0782.53013
[3] Weil, A.: Théorie des points proches sur les variétés différentiables. Colloque de Géometrie Différentielle, C.N.R.S. 52 (1953), 111-117. | · Zbl 0053.24903
[4] Sultanov, A. Ya.: Tensor fields and connections prolongations to Weil bundles. News of Higher Educational Institutions, Math. 9 (1999), 64-72.
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