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Weil bundles; Weil algebra; smooth manifolds
The descriptions of Weil bundles, lifts of functions and vector fields are given. Actions of the automorphisms group of the Whitney sum of algebras of dual numbers on a Weil bundle of the first order are defined.
[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. MR 1202431
[3] Weil, A.: Théorie des points proches sur les variétés différentiables. Colloque de Géometrie Différentielle, C.N.R.S. 52 (1953), 111–117. MR 0061455 | 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. MR 1746634
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