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Quasispaces induced by vector fields measurable in ℝ3

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Abstract

We study some metric functions that are induced by a class of basis vector fields in ℝ3 with measurable coordinates. These functions are proved to be quasimetrics in the domain of definition of the vector fields. Under some natural constraints, the Rashevsky-Chow Theorem and the Ball-Box Theorem are established for the classes of vector fields we consider.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    A. V. Belykh & A. V. Greshnov

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  1. A. V. Belykh
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  2. A. V. Greshnov
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Correspondence to A. V. Greshnov.

Additional information

Original Russian Text Copyright © 2012 Belykh A.V. and Greshnov A.V.

The authors were partially supported by the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” for 2009–2013 (State Contract No. 8206).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 6, pp. 1231–1244, November–December, 2012.

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Belykh, A.V., Greshnov, A.V. Quasispaces induced by vector fields measurable in ℝ3 . Sib Math J 53, 984–995 (2012). https://doi.org/10.1134/S0037446612060031

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  • DOI: https://doi.org/10.1134/S0037446612060031

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