This article is cited in 2 papers

Three-webs $W(1,n,1)$ and associated systems of ordinary differential equations

A. A. Duyunova

Chair of Geometry, Moscow Pedagogical State University, Moscow, Russia

Abstract: We consider a three-web formed by two $n$-parameter families of curves and an one-parameter family of hypersurfaces on a smooth manifold. For such webs we define a family of adapted frames, formulate a system of structural equations, and study differential-geometric objects that arise in differential neighborhoods up to the third order. We prove that each system of ordinary differential equations (SODE) uniquely defines some three-web. This allows us to describe properties of SODE in terms of the corresponding three-web. In particular, we characterize autonomous SODE.

Keywords: multidimensional three-web, system of ordinary differential equations, affine connection.

UDC: 514.763

Received: 10.02.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:2, 37–49

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