An n-dimensional desarguesian space is a metrization of an open subset of the n-dimensional projective space P n as a G-space R whose geodesics fall on projective lines. R is either the entire P n and the geodesics are all isometric to one circle, or R is straight and may be regarded as an open convex set C of the n-dimensional affine space A n with the intersections of the affine Unes with C as geodesies, see Sections 12–14 in G or (8.2) here.
KeywordsGreat Circle Projective Line Nonpositive Curvature Universal Covering Space Open Hemisphere
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