Interpretation of geometry on manifolds as a geometry in a space with projective metric
Contemporary Mathematics. Fundamental Directions, Contemporary problems in mathematics and physics, Tome 65 (2019) no. 1, pp. 1-10.

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In this paper, we give essential concepts of geometry of three-dimensional spaces in vector formulation in an affine-vector space $A_n$.
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A. Artikbaev; S. S. Saitova. Interpretation of geometry on manifolds as a geometry in a space with projective metric. Contemporary Mathematics. Fundamental Directions, Contemporary problems in mathematics and physics, Tome 65 (2019) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/CMFD_2019_65_1_a0/

[1] A. Artykbaev, “Restoration of convex surfaces by outer curvature in the Galilei space”, Math. Digest, 19:2 (1982), 204–224 (in Russian) | MR

[2] L. A. Masal'tsev, “Nil-manifolds cannot be immersed as hypersurfaces in Euclidean spaces”, Math. Notes, 76:6 (2004), 868–873 (in Russian) | DOI | MR | Zbl

[3] B. A. Rozenfel'd, Non-Euclidean Spaces, Nauka, M., 1969 (in Russian)

[4] Scott P., “The geometries of 3-monifolds”, Bull. Lond. Math. Soc., 15:5 (1983), 401–487 | DOI | MR | Zbl