Geodesic
Galilean plane with commutative and nonlinear geometry
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 2, pp. 3-14 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Dolgarev A. I., Dolgarev I. A., “Alternativnoe 2-mernoe deistvitelnoe lineinoe prostranstvo. Gruppa Li zamen bazisov prostranstva”, Vladikavk. mat. zhurn., 10:2 (2008), 9–20 | MR

[2] Dolgarev A. I., Dolgarev I. A., “Alternativnaya affinnaya ploskost”, Vladikavk. mat. zhurn., 9:4 (2007), 4–14 | MR

[3] Rozefeld B. A., Zamakhovskii M. P., Geometriya grupp Li. Simmetricheskie, parabolicheskie i periodicheskie prostranstva, MTsNMO, M., 2003, 560 pp.

[4] Dolgarev A. I., Klassicheskie metody v differentsialnoi geometrii odulyarnykh prostranstv, IITs PGU, Penza, 2005, 306 pp.

[5] Makarova N. M., Dvumernaya neevklidova geometriya s parabolicheskoi metrikoi dlin i uglov, Dis. ... kand. fiz.-mat. nauk, L., 1962, 98 pp.

[6] Yaglom I. M., Printsip otnositelnosti Galileya i neevklidova geometriya, Nauka, M., 1969, 309 pp. | MR

[7] Dolgarev A. I., Elementy differentsialnoi galileevoi geometrii i odul galileevykh preobrazovanii, Srednevolzhskoe mat. obschestvo, Saransk, 2003, 116 pp.

[8] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989, 472 pp. | MR

[9] Dolgarev I. A., Sistemy differentsialnykh uravnenii v chastnykh proizvodnykh dlya poverkhnostei prostranstva Galileya, Dis. ... kand. fiz.-mat. nauk, PGU, Penza, 2007, 119 pp.

[10] Dolgarev I. A., “Nakhozhdenie poverkhnosti v 3-mernom prostranstve Galileya po ee kvadratichnym formam”, Izv. vysshikh uchebnykh zavedenii. Povolzhskii region. Ser. Estestv. nauki, 2006, no. 5, 51–60