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Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems

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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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Authors and Affiliations

  1. Nizhnii Novgorod State University, Nizhnii Novgorod, Russia

    Yu. V. Ershov & E. I. Yakovlev

Authors
  1. Yu. V. Ershov
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  2. E. I. Yakovlev
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Correspondence to Yu. V. Ershov.

Additional information

Original Russian Text Copyright © 2008 Ershov Yu. V. and Yakovlev E. I.

The authors were supported by the Russian Foundation for Basic Research (Grant 06-01-00331-a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 87–100, January–February, 2008.

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Ershov, Y.V., Yakovlev, E.I. Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems. Sib Math J 49, 69–79 (2008). https://doi.org/10.1007/s11202-008-0007-y

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  • DOI: https://doi.org/10.1007/s11202-008-0007-y

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