Induced mappings of the Riemannian spaces of the secondorder approximation(in Russian) 

Author 
pokas@onu.edu.ua
Odessa I. I. Mechnikov National University

Abstract 
For the Riemannian spaces ${\overline{V}}{}_{n}$ and $V_n$ assuming nontrivial geodesic mapping $\gamma$, we have constructed the spaces of the secondorder 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 secondorder approximation// Izvestiya Penz. gos. ped. univ., physicomathematical sciences. 2011. Ή26. P. 173183. (in Russian) 4. Pokas S.M., Tsekhmeystruk L.G. The secondorder approximation for Riemannian space of nonnil constant curvature// Proceedings of International Conference Geometry in Odessa2012. 2012. P. 60. (in Russian) 
Pages 
220224

Volume 
41

Issue 
2

Year 
2014

Journal 
Matematychni Studii

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