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Banaru, "Connections adjoined to the equation y(5) = f(x, y, y', y", y(a), y(4)),,, Smolensk. Gos. Ped. 90, No. 3948-B90 (1990). 2. G. A. Banaru, "Projective connection adjoined to an ordinary differential equation of fifth order," Smolensk. Gos. Ped. 92, No. 847-B92 (1992). 3. A. M. Vasil'ev, "Invariant analytical methods in differential geometry," Dokl. Akad. Nauk SSSR, 79, No. 1, 5-7 (1951). 4. A. M. Vasil'ev, The Theory of Differential-Geometric Structures [In Russian], Mosk. Gos. , Moscow (1987).

The integral curves of the system ~ p + l become geodesic lines on Vn equipped with such a connection, that is, the lines with autoparallel element of tangency of p-order. All invariant properties of the system r p+I and its special classes can be determined in terms of the associated connections. For example, the test of the linearity of the system qap+l with respect to the higher derivatives of the right-hand side of the equations of the system is stated as follows. P r o p o s i t i o n 5. The system ~ P q " iS reducible to a form linear with respect to the higher derivatives of the right-hand side of the system if and only if the part of the components T/a "p-t'l PP be of j2qap+I forming the tensor which is part of the whole curvature tensor of the Cartan connection is equal to zero.

22. V. Glizburg, "About the fundamental group GPn-x of the connection generated by a differential system of higher order," The Third Tartu Univ. Sei. Conf. "Appl. of Topol. in Algebra and Diff. " 2. Tartu Sept. 19-22 (1991); Tartu, 41-46 (1992). 23. V. Glizburg, "Fiber bundles with fundamental-group connection associated with ordinary differential systems of higher order," In: Webs and Quasigroups [In Russian], Tver' (1992), pp. 42-49. 24. E. Cartan, "La geometria de las ecuaciones diferenciales de terces orden," Rev.

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