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作者 Polster, Burkard, author
書名 Geometries on surfaces / Burkard Polster and Gunter Steinke
出版項 Cambridge : Cambridge University Press, 2001
國際標準書號 9780511549656 (electronic bk.)
9780521660587 (hardback)
book jacket
說明 1 online resource (xxii, 490 pages) : digital, PDF file(s)
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
text file PDF rda
系列 Encyclopedia of mathematics and its applications ; volume 84
Encyclopedia of mathematics and its applications ; volume 84
附註 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
The projective, Mobius, 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
主題 Geometry, Projective
Surfaces
Alt Author Steinke, Gunter, 1955- author
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