Geodesic
Three-webs $W(1,n,1)$ and associated systems of ordinary differential equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2012), pp. 43-56.

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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. 
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A. A. Duyunova. Three-webs $W(1,n,1)$ and associated systems of ordinary differential equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2012), pp. 43-56. http://geodesic.mathdoc.fr/item/IVM_2012_2_a4/

[1] Akivis M. A., Goldberg V. V., “O mnogomernykh tri-tkanyakh, obrazovannykh poverkhnostyami raznykh razmernostei”, DAN SSSR, 203:2 (1972), 263–266 | MR | Zbl

[2] Akivis M. A., Goldberg V. V., “O mnogomernykh tri-tkanyakh, obrazovannykh poverkhnostyami raznykh razmernostei”, Tr. geometr. sem., 4, VINITI, M., 1973, 179–204 | MR | Zbl

[3] Akivis M. A., Shelekhov A. M., Geometry and algebra of multidimensional three-webs, Kluwer Academic Publishers, Dordrecht–Boston–London, 1992 | MR | Zbl

[4] Akivis M. A., Shelekhov A. M., Mnogomernye tri-tkani i ikh prilozheniya, Tver. gos. un-t, Tver, 2010

[5] Goldberg V. V., “Transversalno-geodezicheskie, shestiugolnye i gruppovye tri-tkani, obrazovannye poverkhnostyami raznykh razmernostei”, Sb. statei po differents. geometrii, Kalininskii gos. un-t, Kalinin, 1974, 52–64 | MR

[6] Kirichenko V. F., Differentsialno-geometricheskie struktury na mnogoobraziyakh, Mosk. pedagogich. gos. un-t, M., 2003