zbMATH — the first resource for mathematics

Quasigroups on manifolds with trajectories. (English) Zbl 0844.22010
Shelekhov, A. (ed.), Webs and quasigroups. Dedicated to the 60th birthday of Prof. Dr. Vladislav V. Goldberg. Tver: Tver State University. 88-96 (1995).
The notion of a manifold with trajectories is introduced as a one-parameter family of local quasigroups, reflecting properties of solutions of a second order differential equation on a manifold. Some special properties of the differential equation are characterized by the algebraical identities in the manifold with trajectories. Affine connections are associated with a manifold with trajectories. Mechanic systems are considered from this viewpoint.
For the entire collection see [Zbl 0841.00012].
22A99 Topological and differentiable algebraic systems
34A26 Geometric methods in ordinary differential equations
53B99 Local differential geometry
PDF BibTeX Cite