A Remark on the Projective Geometry of Constant Curvature Spaces

Athanase Papadopoulos (1) , Sumio Yamada (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Tohoku University [Sendai]

We highlight the relation between the projective geometries of $n$-dimensional Euclidean, spherical and hyperbolic spaces through the projective models of these spaces in the $n+1$-dimensional Minkowski space, using a cross ratio notion which is proper to each of the three geometries.

Mots clés: cross ratio; non-Euclidean geometry; projective geometry; Minkowski space; generalized Beltrami-Klein model.; generalized Beltrami-Klein model

Domaines: Topologie géométrique [math.GT]

Athanase Papadopoulos, Sumio Yamada. A Remark on the Projective Geometry of Constant Curvature Spaces. 2012. ⟨hal-00732677⟩