# Induced mappings of the Riemannian spaces of the second-order approximation(in Russian)

Author
Odessa I. I. Mechnikov National University
Abstract
For the Riemannian spaces ${\overline{V}}{}_{n}$ and $V_n$ assuming non-trivial geodesic mapping $\gamma$, we have constructed the spaces of the second-order approximation $\widetilde {\overline {V}}{}^{2}_{n}$ and ${\widetilde {V}}{}_{n}^{2}$. We have researched the mapping $\widetilde{\gamma}$, which is induced by the mapping $\gamma$. Also we have obtained the deformation tensor of mapping $\widetilde{\gamma}$ in an explicit form.
Keywords
Riemannian space; geodesic mapping; deformation tensor
Reference
1. Sinyukov N.S., Geodesic mappings of Riemannian spaces. – Moscow, Nauka, 1979. – 225 p. (in Russian)

2. Eisenhart L.P., Riemannian geometry. – Moscow, IL., 1948. – 216 p. (in Russian)

3. Pokas S.M. Groups Li of motions in Riemannian space of second-order approximation// Izvestiya Penz. gos. ped. univ., physico-mathematical sciences. – 2011. – ¹26. – P. 173–183. (in Russian)

4. Pokas S.M., Tsekhmeystruk L.G. The second-order approximation for Riemannian space of non-nil constant curvature// Proceedings of International Conference “Geometry in Odessa-2012”. – 2012. – P. 60. (in Russian)
Pages
220-224
Volume
41
Issue
2
Year
2014
Journal
Matematychni Studii
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