Geodesic
Geodesics on a group of semi-affine transformations of Euclidean plane
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2018), pp. 86-90

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We obtain parameterized representations of geodesics of sub-Riemannian metric on three-dimensional Lie group of semi-affine transformations of the Euclidean plane, i. e., those that act as orientation preserving affine mappings on one axis, and as translations on the other one.
Keywords: Lie groups, sub-Riemannian structure, geodesics. 
@article{IVM_2018_7_a8,
     author = {M. V. Tryamkin},
     title = {Geodesics on a group of semi-affine transformations of {Euclidean} plane},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--90},
     publisher = {mathdoc},
     number = {7},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_7_a8/}
}
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M. V. Tryamkin. Geodesics on a group of semi-affine transformations of Euclidean plane. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2018), pp. 86-90. http://geodesic.mathdoc.fr/item/IVM_2018_7_a8/