Umfang:
1 Online-Ressource (xxii, 490 pages)
,
digital, PDF file(s).
ISBN:
9780511549656
Serie:
Encyclopedia of mathematics and its applications volume 84
Inhalt:
The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, topology, the theory of Lie groups, and many more. The authors detail these connections, some of which are well-known, but many much less so. Acting both as a reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
,
Geometries for Pedestrians -- Geometries of Points and Lines -- Geometries on Surfaces -- Flat Linear Spaces -- Models of the Classical Flat Projective Plane -- Convexity Theory -- Continuity of Geometric Operations and the Line Space -- Isomorphisms, Automorphism Groups, and Polarities -- Topological Planes and Flat Linear Spaces -- Classification with Respect to the Group Dimension -- Constructions -- Planes with Special Properties -- Other Invariants and Characterizations -- Related Geometries -- Spherical Circle Planes -- Models of the Classical Flat Mobius Plane -- Derived Planes and Topological Properties -- Constructions -- Groups of Automorphisms and Groups of Projectivities -- The Hering Types -- Characterizations of the Classical Plane -- Planes with Special Properties -- Subgeometries and Lie Geometries -- Toroidal Circle Planes -- Models of the Classical Flat Minkowski Plane -- Derived Planes and Topological Properties -- Constructions -- Automorphism Groups and Groups of Projectivities -- The Klein-Kroll Types -- Characterizations of the Classical Plane -- Planes with Special Properties -- Subgeometries and Lie Geometries -- Cylindrical Circle Planes -- Models of the Classical Flat Laguerre Plane -- Derived Planes and Topological Properties -- Constructions -- Automorphism Groups and Groups of Projectivities -- The Kleinewillinghofer Types -- Characterizations of the Classical Plane -- Planes with Special Properties -- Subgeometries and Lie Geometries -- Generalized Quadrangles.
Weitere Ausg.:
ISBN 9780521660587
Weitere Ausg.:
ISBN 9780521660587
Weitere Ausg.:
Erscheint auch als Polster, Burkard, 1965 - Geometries on surfaces Cambridge [u.a.] : Cambridge University Press, 2001 ISBN 0521660580
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9780521660587
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Inzidenzgeometrie
;
Topologische Geometrie
DOI:
10.1017/CBO9780511549656
Mehr zum Autor:
Polster, Burkard 1965-
