UNSW books: "Geometries on Surfaces"

Geometries on surfaces Author: Burkard Polster Günter Steinke 1955- Subjects: Geometry, Projective ; Surfaces Description: 1. Geometries for Pedestrians -- 2. Flat Linear Spaces -- 3. Spherical Circle Planes -- 4. Toroidal Circle Planes -- 5. Cylindrical Circle Planes -- 6. Generalized Quadrangles -- 7. Tubular Circle Planes -- App. 1. Tools and Techniques from Topology and Analysis -- App. 2. Lie Transformation Groups. "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 that satisfy an axiom of joining. This book summarises all known major results and open problems related to these classical geometries and their close (non-classical) relatives." "Topics covered include: classical geometries; methods for constructing non-classical geometries; classifications and characterisations of geometries. This work is related to a host of other fields including interpolation theory, convexity, differential geometry, 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 referee for experts and as an accessible introduction for beginners, this book will interest anyone wishing to know more about incidence geometries and the way they interact.

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