Geodesic
Horizontal joinability on $5$-dimensional $2$-step Carnot groups with a codimension $2$ horizontal distribution
Algebra i logika, Tome 62 (2023) no. 2, pp. 205-218

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For a $5$-dimensional $2$-step Carnot group $G_{3,2}$ with a codimension $2$ horizontal distribution, we prove that any two points $u,v\in G_{3,2}$ can be joined on it by a horizontal broken line consisting of at most three segments. A multi-dimensional generalization of this result is given.
Mots-clés : Carnot group
Keywords: codimension horizontal distribution, horizontal broken line. 
@article{AL_2023_62_2_a2,
     author = {R. I. Zhukov and A. V. Greshnov},
     title = {Horizontal joinability on $5$-dimensional $2$-step {Carnot} groups with a codimension $2$ horizontal distribution},
     journal = {Algebra i logika},
     pages = {205--218},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_2_a2/}
}
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R. I. Zhukov; A. V. Greshnov. Horizontal joinability on $5$-dimensional $2$-step Carnot groups with a codimension $2$ horizontal distribution. Algebra i logika, Tome 62 (2023) no. 2, pp. 205-218. http://geodesic.mathdoc.fr/item/AL_2023_62_2_a2/