Induced mappings of the Riemannian
spaces of the second-order approximation

A. V. Krutogolova; S. M. Pokas; L. G. Tsekhmeystruk

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.

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. – №26. – 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)

	Induced mappings of the Riemannian spaces of the second-order approximation(in Russian)
Author	A. V. Krutogolova, S. M. Pokas, L. G. Tsekhmeystruk pokas@onu.edu.ua 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. – №26. – 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
Full text of paper	pdf
Table of content of issue	html

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