Abstract:
We consider a three-web $W(1,n,1)$ formed by two $n$-parametric family of curves and one-parameter family of hypersurfaces on a smooth $(n+1)$-dimensional manifold. For such webs, the family of adapted frames is defined and the structure equations are found, geometric objects arising in the third-order differential neighborhood are investigated. It is showed that every system of ordinary differential equations uniquely defines a three-web $W(1,n,1)$. Thus, there is a possibility to describe some properties of a system of ordinary differential equations in terms of the corresponding three-web $W(1,n,1)$. In particular, autonomous systems of ordinary differential equations are characterized.
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