Authors: Driuma Valeriu
Abstract
Some properties of Riemannian and Einstein-Weyl spaces associated with the second order nonlinear differential equations
$y''+a_{1}(x,y){y'}^3+3a_{2}(x,y){y'}^2+\mathbreak+3a_{3}(x,y)y'+a_{4}(x,y)=0$
with arbitrary coefficients $a_{i}(x,y)$ and dual equations $b''=g(a,b,b')$ with function $g(a,b,b')$ satisfying the partial differential equation
$g_{aacc}+2cg_{abcc}+2gg_{accc}+c^2g_{bbcc}+2cgg_{bccc}+
g^2g_{cccc}+(g_a+cg_b)g_{ccc}-4g_{abc}-\mathbreak -4cg_{bbc} -cg_{c}g_{bcc}-
3gg_{bcc}-g_cg_{acc}+ 4g_cg_{bc}-3g_bg_{cc}+6g_{bb} =0$
are considered.
Institutul de Matematică al Academiei de Ştiinţe a Moldovei
str. Academiei 5, Chişinău MD-2028, Moldova
E-mail: ;