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This article is cited in 3 scientific papers (total in 3 papers)
Horizontal joinability in canonical 3-step Carnot groups with corank 2 horizontal distributions
A. V. Greshnova, R. I. Zhukovb a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Abstract:
We prove that on each 2-step Carnot group with a corank 1 horizontal distribution two arbitrary points can be joined with a horizontal broken line consisting of at most 3 segments, while on every canonical 3-step Carnot group $\Bbb G$ with a corank 2 horizontal distribution two arbitrary points can be joined with a horizontal broken line consisting of at most 7 segments. We show that two arbitrary points in the center of $\Bbb G$ are joined by infinitely many horizontal broken lines with 4 segments. Here by a segment of a horizontal broken line we mean a segment of an integral line of some left-invariant horizontal vector field that is a linear combination of left-invariant horizontal basis vector fields of the Carnot group.
Keywords:
left-invariant basis vector fields, horizontal broken line, Rashevskii–Chow theorem, Carnot group.
Received: 06.10.2020 Revised: 04.06.2021 Accepted: 11.06.2021
Citation:
A. V. Greshnov, R. I. Zhukov, “Horizontal joinability in canonical 3-step Carnot groups with corank 2 horizontal distributions”, Sibirsk. Mat. Zh., 62:4 (2021), 736–746; Siberian Math. J., 62:4 (2021), 598–606
Linking options:
https://www.mathnet.ru/eng/smj7591 https://www.mathnet.ru/eng/smj/v62/i4/p736
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