Geodesic
Galilean plane with commutative and nonlinear geometry
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 2, pp. 3-14

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Galilean distance between two points on the plane with nonlinear geometry is introduced. A specified physical interpretation of such a plane is indicated. The curvature of regular curves is defined and it is proved that the curvature function determines uniquely the curve under consideration. 
@article{VMJ_2010_12_2_a0,
     author = {A. I. Dolgarev and I. A. Dolgarev},
     title = {Galilean plane with commutative and nonlinear geometry},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_2_a0/}
}
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A. I. Dolgarev; I. A. Dolgarev. Galilean plane with commutative and nonlinear geometry. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 2, pp. 3-14. http://geodesic.mathdoc.fr/item/VMJ_2010_12_2_a0/