Geodesic
Curves in the geometry of a special extension of Euclidean space
Matematičeskie zametki SVFU, Tome 29 (2022) no. 1, pp. 3-12 Cet article a éte moissonné depuis la source Math-Net.Ru

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In modern mathematics, the use of geometries with a maximum group of motions is of particular importance. There are many classifications of such geometries, one of which contains the geometry of a special extension of Euclidean space. This geometry belongs to the family of geometries with a degenerate Riemannian metric, but at the same time admits a group of motions of maximum dimension. This paper investigates the metric properties of the geometry of a special extension of Euclidean space. The concept of the length of a curve in such a geometry is introduced. The curve of the minimum length is found. It is proved that a segment in a horizontal hyperplane has the minimum length. The Christoffel symbols of the geometry of a special extension of Euclidean space are calculated.
Keywords: geometry of a special extension of Euclidean space, degenerate Riemannian metric, curve length. 
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     author = {V. A. Kyrov},
     title = {Curves in the geometry of a special extension of {Euclidean} space},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {3--12},
     year = {2022},
     volume = {29},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2022_29_1_a0/}
}
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V. A. Kyrov. Curves in the geometry of a special extension of Euclidean space. Matematičeskie zametki SVFU, Tome 29 (2022) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/SVFU_2022_29_1_a0/