Geometry of Minkowski planes and spaces [Elektronische Ressource] : selected topics / vorglegt von Senlin Wu

Geometry of Minkowski Planesand Spaces– Selected TopicsD I S S E R T A T I O Nzur Erlangung des akademischen GradesDoctor rerum naturalium(Dr. rer. nat.)Vorgelegt von M. Sc. Senlin Wugeboren am 16.01.1982 in ShanXi Provinz, VR ChinaGutachter: Prof. Dr. Horst Martini (TU Chemnitz)Prof. Dr. Gunter Weiß(TU Dresden)Prof. Dr. Eike Hertel (Friedrich-Schiller-Universitaet Jena)Tag der Verteidigung: 29. 01. 20091AbstractThe results presented in this dissertation refer to the geometry of Minkowskispaces, i.e., of real finite-dimensional Banach spaces.First we study geometric properties of radial projections of bisectors inMinkowski spaces, especially the relation between the geometric structure ofradial projections and Birkhoff orthogonality. As an application of our resultsit is shown that for any Minkowski space there exists a number, which plays√somehow the role that 2 plays in Euclidean space. This number is referredto as the critical number of any Minkowski space. Lower and upper bounds onthe critical number are given, and the cases when these bounds are attained arecharacterized. Moreover, with the help of the properties of bisectors we showthat a linear map from a normed linear space X to anothernormed linear spaceY preservesisoscelesorthogonalityif andonlyif itisascalarmultiple ofalinearisometry.