Konrad, Angelika Space-time-world and hyperbolic geometry. (Raum-Zeit-Welt und hyperbolische Geometrie.) (German) Zbl 0871.51012 TUM, Math. Inst., Beitr. Geom. Algebra M 9412(29), ii, 175 p. (1994). The paper is a compact manual on selected chapters of higher geometry and an introduction of fundamental tools in special relativity. The whole exposition is well accorded to the Erlangen Program. An advanced matrix calculus and abstract algebras are applied. Hyperbolic geometry of dimension 2 is introduced as an axiomatic theory, then it is developed in an analytical way by means of the model of Klein. Reviewer: A.Szybiak (Waterloo/Ontario) MSC: 51M10 Hyperbolic and elliptic geometries (general) and generalizations 51-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry 83-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory 83A05 Special relativity 15A15 Determinants, permanents, traces, other special matrix functions 15A04 Linear transformations, semilinear transformations Keywords:similitude; isometry; Lorentz group; world point; Minkowski world; \(K\)-loop; place distance; time distance; orthochrom; antiton; special relativity PDFBibTeX XMLCite \textit{A. Konrad}, TUM, Math. Inst., Beitr. Geom. Algebra M 9412(29), ii, 175\,p. (1994; Zbl 0871.51012)