TY - CHAP
T1 - Cayley-Klein Spaces
AU - Bobenko, Alexander I.
AU - Lutz, Carl O.R.
AU - Pottmann, Helmut
AU - Techter, Jan
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85118583338&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-81847-0_4
DO - 10.1007/978-3-030-81847-0_4
M3 - Chapter
AN - SCOPUS:85118583338
T3 - SpringerBriefs in Mathematics
SP - 27
EP - 36
BT - SpringerBriefs in Mathematics
PB - Springer Science and Business Media B.V.
ER -