On canonical first-type almost geodesic mappings of affinely connected spaces that preserve the Riemann tensor

V. E. Berezovskii ; S. V. Leshchenko ; J. Mikeš

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 23-33.

Résumé

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.

Détail

Keywords: almost geodesic mapping, basic equation, space of affine connection.

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