Minkowski Geometry

ISBN-13: 9780521404723 / Angielski / Twarda / 1996 / 368 str.

A. C. Thompson; Anthony C. Thompson; G. -C Rota

Opis

This is a comprehensive treatment of Minkowski geometry. 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 characterizations 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.

Recenzje

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

Spis treści

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.