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Relèvements des champs de vecteurs aux fibrés naturels. (French) Zbl 0532.53027

The author defines the notion of quasi-liftings of vector fields to natural bundles and proves that this definition generalizes the notion of liftings of vector fields to tangent bundles, to tangent bundles of higher order, to tangent bundles of \(p^ r-velocities\) due to K. Yano and S. Ishihara [Tangent and cotangent bundles. Differential geometry (1973; Zbl 0262.53024)] and the reviewer [Nagoya Math. J. 32, 67-108 (1968; Zbl 0159.234); ibid. 40, 13-31 (1970; Zbl 0208.244); ibid. 40, 85-97 (1970; Zbl 0208.501)]. The stated results in this paper are announcements of the contents in the author’s paper [Diss. Math. 212, 55 p. (1983; Zbl 0517.53016)].
Reviewer: A.Morimoto

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53B99 Local differential geometry
55R65 Generalizations of fiber spaces and bundles in algebraic topology