Sub-Riemannian geometry for vector fields of minimal smoothness (Q1048507)
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scientific article; zbMATH DE number 5656089
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sub-Riemannian geometry for vector fields of minimal smoothness |
scientific article; zbMATH DE number 5656089 |
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Sub-Riemannian geometry for vector fields of minimal smoothness (English)
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12 January 2010
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This paper investigates the geometric properites of Carnot-Caratheodory spaces for vector fields of minimal smoothness (of lcass \(C^1\)). Using the ``distance'' defined by Definition 4, the authors consider the convergence of \(C^1-\)vector fields associated with Box\((x, r)\), and get some new proofs of Gromov's Theorem [\textit{M. Gromov}, in: Sub-Riemannian geometry, Birkhäuser, Basel, 79--318 (1996; Zbl 0578.32044)]. The results posed in the present paper are interesting.
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sub-Riemannian geometry
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minimal
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Gromov's theorem
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