Geodesic
Geodesics in the Heisenberg group: an elementary approach
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 177-188

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We derive in an elementary way the shape of geodesics of the left invariant Carnot–Caratheodory–Finsler metrics on the Heisenberg group. The only existing proof of this result was given by V. N. Berestovskii, using the Pontryagin maximum principle.
Keywords: Heisenberg group, geodesic, Isoperimetric Problem. 
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     title = {Geodesics in the {Heisenberg} group: an elementary approach},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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G. A. Noskov. Geodesics in the Heisenberg group: an elementary approach. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 177-188. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a12/