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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 2, Pages 259–292
(Mi smj855)
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This article is cited in 16 scientific papers (total in 16 papers)
Metrics and tangent cones of uniformly regular Carnot–Carathéodory spaces
A. V. Greshnov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
Given a uniformly regular Carnot–Carathéodory space, we prove equivalence of the quasimetrics generated by various bases of vector fields which agree with filtration of the space. We prove a theorem on a nilpotent tangent cone for a uniformly regular Carnot–Carathéodory space furnished with quasimetrics. As a consequence, we obtain a theorem on isomorphism of nilpotent tangent cones defined at a common distinguished point.
Keywords:
Carnot–Caratheodory space, nilpotent group.
Received: 27.09.2005
Citation:
A. V. Greshnov, “Metrics and tangent cones of uniformly regular Carnot–Carathéodory spaces”, Sibirsk. Mat. Zh., 47:2 (2006), 259–292; Siberian Math. J., 47:2 (2006), 209–238
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https://www.mathnet.ru/eng/smj855 https://www.mathnet.ru/eng/smj/v47/i2/p259
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