The Riemann Extensions in Theory of Ordinary Differential Equations and their Applications
| dc.creator | Dryuma, Valery S. | |
| dc.date | 2003-03-11 | |
| dc.date.accessioned | 2026-07-07T05:34:36Z | |
| dc.date.available | 2026-07-07T05:34:36Z | |
| dc.description | Some properties of the 4-dim Riemannian spaces with the metrics $$ ds^2=2(za_3-ta_4)dx^2+4(za_2-ta_3)dxdy+2(za_1-ta_2)dy^2+2dxdz+2dydt $$ associated with the second order nonlinear differential equations $$ y''+a_{1}(x,y){y'}^3+3a_{2}(x,y){y'}^2+3a_{3}(x,y)y'+a_{4}(x,y)=0 $$ with arbitrary coefficients $a_{i}(x,y)$ and 3-dim Einstein-Weyl spaces connected with dual equations $b''=g(a,b,b')$ where the function $g(a,b,b')$ satisfied the partial differential equation $$ g_{aacc}+2cg_{abcc}+2gg_{accc}+c^2g_{bbcc}+2cgg_{bccc}+ g^2g_{cccc}+(g_a+cg_b)g_{ccc}-4g_{abc}- $$ $$ -4cg_{bbc} -cg_{c}g_{bcc}- 3gg_{bcc}-g_cg_{acc}+ 4g_cg_{bc}-3g_bg_{cc}+6g_{bb} =0 $$ are considered. Some applications to the studying of the nonlinear dynamical systems and the Riemann manifolds in General Relativity are discussed. | |
| dc.description | 37 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/nlin/0303023 | |
| dc.identifier | http://arxiv.org/abs/nlin/0303023 | |
| dc.identifier | Theoretical and Mathematical Physics, v.128 (1), (2001), 15-26 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80428 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | The Riemann Extensions in Theory of Ordinary Differential Equations and their Applications | |
| dc.type | text |