Geodesic
On canonical first-type almost geodesic mappings of affinely connected spaces that preserve the Riemann tensor
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 23-33

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In this paper, we obtain general equations for canonical first-type almost geodesic mappings of affinely connected spaces under which the Riemann tensor is preserved. These equations are reduced to a closed system of Cauchy-type equations in covariant derivatives. The number of essential parameters on which the general solution of the resulting system of equations depends is established. A particular case of such mappings is considered and examples of almost geodesic mappings of the first type of flat space onto flat space are given.
Keywords: almost geodesic mapping, basic equation, space of affine connection. 
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     title = {On canonical first-type almost geodesic mappings of affinely connected spaces that preserve the {Riemann} tensor},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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V. E. Berezovskii; S. V. Leshchenko; J. Mikeš. On canonical first-type almost geodesic mappings of affinely connected spaces that preserve the Riemann tensor. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 23-33. http://geodesic.mathdoc.fr/item/INTO_2023_226_a2/