Geodesic
Infinitesimal affine transformations of the space $(T^0_2(M_n),\nabla^H)$ over a maximally movable space $(M_n,\nabla)$ which is not projectively flat.
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 132-137 
O. A. Monakhova. Infinitesimal affine transformations of the space $(T^0_2(M_n),\nabla^H)$ over a maximally movable space $(M_n,\nabla)$ which is not projectively flat.. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 132-137. http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a11/
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     title = {Infinitesimal affine transformations of the space $(T^0_2(M_n),\nabla^H)$ over a~maximally movable space $(M_n,\nabla)$ which is not projectively flat.},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {132--137},
     year = {2005},
     volume = {147},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a11/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the bundle $T^2_0M$ of tensors of type $(2,0)$ over a maximally movable affinely connected space $(M,\nabla)$. On the total space of this bundle we take the horizontal lift $\nabla^C$ of the connection $\nabla$ and construct decomposition for infinitesimal affine transformations of $\nabla^C$. Also we find the dimension of the Lie algebra of infinitesimal transformations of this space.

[1] Egorov I. P., Dvizheniya v prostranstvakh affinnoi svyaznosti, Kazan, 1965, 206 pp. | MR

[2] Monakhova O. A., “Gorizontalnyi lift svyaznosti v rassloenii dvazhdy kovariantnykh tenzorov”, Dvizheniya v obobschennykh prostranstvakh, Penza, 2002, 168–172

[3] Yano K., Ishihara S., Tangent and cotangent bundles. Differential geometry, New York, 1973 | MR