Thompson A. C.  Minkowski geometry

Название: 
Minkowski geometry 
Автор: 
Thompson A. C. 
Категория: 
Математика

Тип: 
Книга 
Дата: 
31.12.2008 00:05:44 
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91 
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Описание: 
I
Minkowski geometry is a nonEuclidean geometry in a finite number of dimensions thai is different from elliptic and hyperbolic geometry (and from the Minkowskian geometry of spacetime). Here the linear structure is the same as the Euclidean one but distance is not "uniform" in all directions. Instead of the usual sphere in Euclidean space, the unit ball is a general symmetric convex set. Therefore, although the parallel axiom is valid, Pythagoras' theorem is not.
This book begins by presenting the topological properties of Minkowski spaces, including the existence and essential uniqueness of Haar measure, followed by the fundamental metric properties  the group of isometries, the existence of certain ; bases and the existence of the Lowner ellipsoid. This is followed by characterf izations of Euclidean space among normed spaces and a full treatment of twoj dimensional spaces. The three central chapters present the theory of area and volume in normed spaces. The author describes the fascinating geometric interj play among the isoperimetrix (the convex body which solves the isoperimetric ! problem), the unit ball and their duals, and the ways in which various roles of  the ball in Euclidean space are divided among them. The next chapter deals with i trigonometry in Minkowski spaces and the last one takes a brief look at a number i' of numerical parameters associated with a normed space, including J. J. SchaTfer's . ideas on the intrinsic geometry of the unit sphere. Each chapter ends with a section : of historical notes, and the book ends with a list of 50 unsolved problems. ! Minkowski Geometry will appeal to students and researchers interested in ge: ometry, convexity theory and functional analysis. 
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