Geodesic
On preservation of the Riemann tensor with respect to some mappings of space with affine connection
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2018), pp. 3-10

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This paper is devoted to geodesic and almost geodesic mappings of spaces with affine connection. We find conditions which ensure that the Riemann tensor is an invariant geometric object with respect to the studied mappings. In this work we present an example of the non-trivial geodesic mappings between the flat spaces.
Keywords: Riemann tensor, geodesic mapping, almost geodesic mapping. 
@article{IVM_2018_9_a0,
     author = {V. E. Berezovskii and L. E. Kovalev and J. Mike\v{s}},
     title = {On preservation of the {Riemann} tensor with respect to some mappings of space with affine connection},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--10},
     publisher = {mathdoc},
     number = {9},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_9_a0/}
}
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V. E. Berezovskii; L. E. Kovalev; J. Mikeš. On preservation of the Riemann tensor with respect to some mappings of space with affine connection. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2018), pp. 3-10. http://geodesic.mathdoc.fr/item/IVM_2018_9_a0/