Geodesic
Solution of the embedding problem for two-dimensional and three-dimensional geometries of local maximum mobility
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 124-143.

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In modern geometry, the study of the geometries of maximum mobility is of great importance. Some of these geometries are well studied (for example, the Euclidean and Lobachevsky geometries, pseudo-Euclidean, symplectic, spherical geometry, etc.), while others (for example, Helmholtz and pseudo-Helmholtz geometries) have not yet attracted active attention of researchers. There is still no complete classification of the geometries of maximum mobility. In this work, we present some results concerning the classification problem for two- and three-dimensional geometries of local maximum mobility. This problem is reduced to functional equations of a special form and is solved by the embedding method in the class of analytic functions.
Keywords: geometry of maximum mobility, functional equation.
Mots-clés : motion group 
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V. A. Kyrov. Solution of the embedding problem for two-dimensional and three-dimensional geometries of local maximum mobility. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 124-143. http://geodesic.mathdoc.fr/item/INTO_2021_194_a11/

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