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Sibirsk. Mat. Zh., 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

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

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English version:
Siberian Mathematical Journal, 2003, 44:6, 1085–1090

Bibliographic databases:

UDC: 519.9,514.7:519.46
Received: 24.09.2002

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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\by R.~R.~Faizullin
\paper On connection between the nonholonomic metric on the Heisenberg group and the Grushin metric
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1377--1384
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\elib{http://elibrary.ru/item.asp?id=5219470}
\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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Berestovskii, “Similarly homogeneous locally complete spaces with an intrinsic metric”, Russian Math. (Iz. VUZ), 48:11 (2004), 1–19  mathnet  mathscinet  elib
    2. A. O. Remizov, “On geodesics in metrics with singularities of the Klein type”, Russian Math. Surveys, 65:1 (2010), 180–182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. A. V. Greshnov, “The geometry of $cc$-balls and the constants in the Ball-Box theorem on Heisenberg group algebras”, Siberian Math. J., 55:5 (2014), 849–865  mathnet  crossref  mathscinet  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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