Geodesic
Sub-Riemannian geodesics on the multidimensional Heisenberg group
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 2, Tome 180 (2020), pp. 74-84

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In this paper, we study the structure of truncated connections on the multidimensional Heisenberg group endowed with a left-invariant sub-Riemannian structure. We find that sub-Riemannian geodesics are parabolas whose orthogonal projections onto the corresponding contact planes are straight lines. In addition to such parabolas, some straight lines lying in contact planes are also geodesics.
Keywords: Heisenberg group, sub-Riemannian structure, left-invariant contact metric structure, geodesic. 
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     author = {V. I. Panzhenskii and O. P. Surina},
     title = {Sub-Riemannian geodesics on the multidimensional {Heisenberg} group},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {74--84},
     publisher = {mathdoc},
     volume = {180},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_180_a10/}
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V. I. Panzhenskii; O. P. Surina. Sub-Riemannian geodesics on the multidimensional Heisenberg group. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 2, Tome 180 (2020), pp. 74-84. http://geodesic.mathdoc.fr/item/INTO_2020_180_a10/