說明 
1 online resource (xxii, 490 pages) : digital, PDF file(s) 

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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 KleinKroll 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 pointline 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 wellknown, 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 pointline geometries and the way they interact 
主題 
Geometry, Projective


Surfaces

Alt Author 
Steinke, Gunter, 1955 author

