This article is cited 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.

UDC: 519.9,514.7:519.46

Received: 24.09.2002

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

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