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On Preservation of the Riemann Tensor With Respect to Some Mappings of Affinely Connected Space

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Abstract

This paper is devoted to geodesic and almost geodesic mappings of affinely connected spaces. 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 a non-trivial geodesic mapping between the flat spaces.

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Authors and Affiliations

  1. Uman National University of Horticulture, ul. Institutskaya 1, Uman, Cherkasy Obl., 20305, Ukraine

    V. E. Berezovskii & L. E. Kovalev

  2. Palacký University 17 listopadu 12, Olomouc, 77146, Czech Republic

    J. Mikeš

Authors
  1. V. E. Berezovskii
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  2. L. E. Kovalev
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  3. J. Mikeš
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Corresponding author

Correspondence to V. E. Berezovskii.

Additional information

Original Russian Text © V.E. Berezovskii, L.E. Kovalev, J. Mikeš, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 9, pp. 3–10.

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Berezovskii, V.E., Kovalev, L.E. & Mikeš, J. On Preservation of the Riemann Tensor With Respect to Some Mappings of Affinely Connected Space. Russ Math. 62, 1–6 (2018). https://doi.org/10.3103/S1066369X18090013

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