On one class of Lipschitz vector fields in a"e3

被引：2
|
作者：
Greshnov, A. V. [1 ,2 ]
机构：
[1] Sobolev Inst Math, Novosibirsk, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2010年 / 51卷 / 03期
关键词：
Lipschitz vector field; quasimetric; generalized triangle inequality; horizontal curve; CARNOT-CARATHEODORY SPACES; METRICS; DIFFERENTIABILITY; GEOMETRY; MAPPINGS;
D O I：
10.1007/s11202-010-0042-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Under consideration are some continuous metric functions induced by one class of Lipschitz vector fields in a"e(3). These functions are showed to be quasimetrics within the domain of definition of the vector fields. We prove some analogs of the Rashevsky-Chow Theorem and the Ball-Box Theorem under some restriction on the class of vector fields. The methods of proofs do not use the existence of the nilpotent tangent cone.
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页码：410 / 418
页数：9
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