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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 6, Pages 1377–1384 (Mi smj1263)  
This article is cited in 3 scientific papers (total in 3 papers)

On connection between the nonholonomic metric on the Heisenberg group and the Grushin metric

R. R. Faizullin

Omsk State University
Full-text PDF (174 kB) Citations (3)
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Abstract: The purpose of this paper is to compute geodesics on the Grushin plane and examine an assertion on connection between spheres of the Grushin plane and spheres of the Heisenberg group. The assertion turns out to require correction that the spheres of the Heisenberg group are directly obtained by rotation of the Grushin spheres. We find a modified Grushin metric for which the last assertion holds. Also, we prove several theorems about connections between the Grushin plane and Heisenberg group.
Keywords: geodesic, Riemannian metric, Heisenberg group, Grushin plane.
Received: 24.09.2002
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 6, Pages 1085–1090
DOI: https://doi.org/10.1023/B:SIMJ.0000007484.09296.98
Bibliographic databases:
UDC: 519.9,514.7:519.46
Language: Russian
Citation: R. R. Faizullin, “On connection between the nonholonomic metric on the Heisenberg group and the Grushin metric”, Sibirsk. Mat. Zh., 44:6 (2003), 1377–1384; Siberian Math. J., 44:6 (2003), 1085–1090
Citation in format AMSBIB
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\paper On connection between the nonholonomic metric on the Heisenberg group and the Grushin metric
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\pages 1377--1384
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\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 1085--1090
\crossref{https://doi.org/10.1023/B:SIMJ.0000007484.09296.98}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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