Cayley-Klein Spaces

Alexander I. Bobenko*, Carl O.R. Lutz, Helmut Pottmann, Jan Techter

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageEnglish (US)
Title of host publicationSpringerBriefs in Mathematics
PublisherSpringer Science and Business Media B.V.
Number of pages10
StatePublished - 2021

Publication series

NameSpringerBriefs in Mathematics
ISSN (Print)2191-8198
ISSN (Electronic)2191-8201

ASJC Scopus subject areas

  • General Mathematics


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