Canonical decomposition of projective and affine killing vectors on the tangent bundle

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).Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 247–258, February, 1976.