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.
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Faizullin, R.R. On Connection Between the Nonholonomic Metric on the Heisenberg Group and the Grushin Metric. Siberian Mathematical Journal 44, 1085–1090 (2003). https://doi.org/10.1023/B:SIMJ.0000007484.09296.98
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DOI: https://doi.org/10.1023/B:SIMJ.0000007484.09296.98