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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 1, Pages 87–100 (Mi smj1824)  
This article is cited in 5 scientific papers (total in 5 papers)

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

Yu. V. Ershov, E. I. Yakovlev

N. I. Lobachevski State University of Nizhni Novgorod
Full-text PDF (337 kB) Citations (5)
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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.
Keywords: Riemannian manifold, path space, generalized distance function, gyroscopic system, many-valued functional, extremal.
Received: 25.10.2006
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 2, Pages 69–79
DOI: https://doi.org/10.1007/s11202-008-0007-y
Bibliographic databases:
UDC: 514.76+515.165.7
Language: Russian
Citation: Yu. V. Ershov, E. I. Yakovlev, “Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems”, Sibirsk. Mat. Zh., 49:1 (2008), 87–100; Siberian Math. J., 49:2 (2008), 69–79
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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