Geodesic
The analytical method for embedding multidimensional
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 741-758

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As is known, the geometry of the local maximum mobility is an $n$-dimensional pseudo-Euclidean geometry. In this paper, we find all the $(n+1)$-dimensional geometries of the local maximal mobility whose metric functions contain the metric function of pseudo-Euclidean geometry as an argument. Such geometries are: $(n+1)$-dimensional pseudo-Euclidean geometry, $(n+1)$-dimensional special extension of $n$-dimensional pseudo-Euclidean geometry, $(n+1)$-dimensional geometry of constant curvature on a pseudo sphere.
Keywords: pseudo-Euclidean geometry, functional equation, differential equation, metric function. 
@article{SEMR_2018_15_a45,
     author = {V. A. Kyrov},
     title = {The analytical method for embedding multidimensional},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {741--758},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a45/}
}
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V. A. Kyrov. The analytical method for embedding multidimensional. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 741-758. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a45/