Canonical decomposition of projective and affine killing vectors on the tangent bundle
Matematičeskie zametki, Tome 19 (1976) no. 2, pp. 247-258.

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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-Euclidean space which is maximally homogeneous (in the sense of affine collineations) there exist affine collineations permuting the fibers of $T(M)$.
@article{MZM_1976_19_2_a9,
     author = {F. I. Kagan},
     title = {Canonical decomposition of projective and affine killing vectors on the tangent bundle},
     journal = {Matemati\v{c}eskie zametki},
     pages = {247--258},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a9/}
}
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F. I. Kagan. Canonical decomposition of projective and affine killing vectors on the tangent bundle. Matematičeskie zametki, Tome 19 (1976) no. 2, pp. 247-258. http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a9/