cahtНаучный вестник МГТУ ГАCivil Aviation High Technologies2079-06192542-0119Moscow State Technical University of Civil Aviation (MSTU CA)caht-239Research ArticleСтатьиАффинная связность, присоединенная к ткани W(1, n, 1)Affine connection adjoined to web W(1, n, 1)ДуюноваА. А.DuyunovaA. A.noemail@neicon.ru2014071120160207100109Copyright © Дуюнова А.А., 20162016Дуюнова А.А.Duyunova A.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://avia.mstuca.ru/jour/article/view/239

В статье к три-ткани W(1,n,1) и системе дифференциальных уравнений присоединяется совместимая аффинная связность без кручения, названая канонической связностью системы ОДУ. Компоненты тензора кривизны этой связности вычислены через функции, определяющие систему дифференциальных уравнений, и записан вид системы ОДУ с нулевым тензором кривизны.

The 3-web and the system of differential equations are adjoined with an associated affine torsion-free connection (the so called canonical connection of an ordinary differential equations’ system). Components of the torsion tensor of this connection are expressed through the functions defining the system of differential equations. A general form of the system of differential equations with the zero torsion tensor is obtained.

multidimensional three-websystem of ordinary differential equationsaffine connectionmultidimensional three-websystem of ordinary differential equationsaffine connectionReferencesAkivis M., Goldberg V. On multidimensional three-webs formed by surfaces of different dimensions: Dokl. AN USSR. - 1972. - V. 203. - № 2. - P. 263-266.Akivis M., Goldberg V. On multidimensional three-webs formed by surfaces of different dimensions: Dokl. AN USSR. - 1972. - V. 203. - № 2. - P. 263-266.Akivis M., Goldberg V. On multidimensional three-webs formed by surfaces of different dimensions: Trudy geometr. seminara VINITI AN USSR. - 1973. - V. 4. - P. 179-204.Akivis M., Goldberg V. On multidimensional three-webs formed by surfaces of different dimensions: Trudy geometr. seminara VINITI AN USSR. - 1973. - V. 4. - P. 179-204.Duyunova A. Three-webs defined by systems of ordinary differential equations // Fundamental and applied mathematics. - 2010. - V. 16. - №. 2. - P. 13-31.Duyunova A. Three-webs defined by systems of ordinary differential equations // Fundamental and applied mathematics. - 2010. - V. 16. - №. 2. - P. 13-31.Kirichenko V. Differential geometric structures on manifolds. - M.: Moscow State Pedagogical University, 2003.Kirichenko V. Differential geometric structures on manifolds. - M.: Moscow State Pedagogical University, 2003.

The authors declare that there are no conflicts of interest present.