Abstract
In Klein’s Erlangen program Euclidean and non-Euclidean geometries are considered as subgeometries of projective geometry. Projective models for, e.g., hyperbolic, deSitter, and elliptic space can be obtained by using a quadric to induce the corresponding metric [Kle1928]. In this section we introduce the corresponding general notion of Cayley-Klein spaces and their groups of isometries, see, e.g., [Kle1928, Bla1954, Gie1982]. We put a particular emphasis on the description of hyperplanes, hyperspheres, and their mutual relations.
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Bobenko, A.I., Lutz, C.O.R., Pottmann, H., Techter, J. (2021). Cayley-Klein Spaces. In: Non-Euclidean Laguerre Geometry and Incircular Nets. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-81847-0_4
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DOI: https://doi.org/10.1007/978-3-030-81847-0_4
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