Abstract
For an affine connection on the tangent bundle T(M) obtained by lifting an affine connection on M, the structure of vector fields on T(M) which generate local one-parameter groups of projective and affine collineations is described. On the T(M) of a complete irreducible Riemann manifold, every projective collineation is affine. On the T(M) of a projectively Euclidean space, every affine collineation preserves the fibration of T(M), and on the T(M) of a projectively non-Duclidean space which is maximally homogeneous (in the sense of affine collineations) there exist affine collineations permuting the fibers of T(M).
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Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 247–258, February, 1976.
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Kagan, F.I. Canonical decomposition of projective and affine killing vectors on the tangent bundle. Mathematical Notes of the Academy of Sciences of the USSR 19, 146–152 (1976). https://doi.org/10.1007/BF01098748
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DOI: https://doi.org/10.1007/BF01098748