Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems |
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Authors: | Yu V Ershov E I Yakovlev |
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Institution: | (1) Nizhnii Novgorod State University, Nizhnii Novgorod, Russia |
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Abstract: | We use the homology groups of the path space of an arbitrary Riemannian manifold to define some analogs of the distance function and study their main properties. For the natural systems with gyroscopic forces we prove an existence theorem for solutions to the two-point boundary value problem, which complements the results of 1]. We apply the geodesic modeling method of 1, 2], using the generalized distance functions. |
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Keywords: | Riemannian manifold path space generalized distance function gyroscopic system many-valued functional extremal |
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