Geodesic
On Metric Equivalence of Functions on the Lobachevski Plane
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 54-59
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We find necessary and sufficient conditions for functions to be equivalent with respect to the isometry group of the Lobachevski plane.
Keywords: differential invariants, invariant derivations, Lobachevski plane, isometry. 
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N. G. Konovenko; V. V. Lychagin. On Metric Equivalence of Functions on the Lobachevski Plane. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 54-59. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a5/

[1] Klein F., “Sravnitelnoe obozrenie noveishikh geometricheskikh issledovanii”, Ob osnovaniyakh geometrii, 1872, 399–434

[2] Vinogradov A. M., Krasilschik I. S., Lychagin V. V., Vvedenie v geometriyu nelineinykh differentsialnykh uravnenii, Nauka, M., 1986, 336 pp. | MR