Minkowski Geometry

The first comprehensive treatment of Minkowski geometry since the 1940's

A. C. Thompson (Author)

9780521404723, Cambridge University Press

Hardback, published 28 June 1996

368 pages, 50 b/w illus.
24.2 x 16.4 x 2.5 cm, 0.718 kg

'This is a comprehensive monograph that will serve well both as an introduction and as a reference work.' Monatshefte für Mathematik

Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940s. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterisations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces, a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis.

1. The algebraic properties of linear spaces and of convex sets
2. Norms and norm topologies
3. Convex bodies
4. Comparisons and contrasts with Euclidean space
5. Two dimensional Minkowski spaces
6. The concept of area and content
7. Special properties of the Holmes-Thompson definition
8. Special properties of the Busemann definition
9. Trigonometry
10. Various numerical parameters.

Subject Areas: Geometry [PBM]