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OverviewA comprehensive approach to qualitative problems in intrinsic differential geometry, this text for upper-level undergraduates and graduate students emphasizes cases in which geodesics possess only local uniqueness properties--and consequently, the relations to the foundations of geometry are decidedly less relevant, and Finsler spaces become the principal subject.This direct approach has produced many new results and has materially generalized many known phenomena. Author Herbert Busemann begins with an explanation of the basic concepts, including compact metric spaces, convergence of point sets, motion and isometry, segments, and geodesics. Subsequent topics include Desarguesian spaces, with discussions of Riemann and Finsler spaces and Beltrami's theorem; perpendiculars and parallels, with examinations of higher-dimensional Minkowskian geometry and the Minkowski plane; and covering spaces, including locally isometric space, the universal covering space, fundamental sets, free homotopy and closed geodesics, and transitive geodesics on surfaces of higher genus. Concluding chapters explore the influence of the sign of the curvature on the geodesics, and homogenous spaces, including those with flat bisectors. Full Product DetailsAuthor: Herbert BusemannPublisher: Dover Publications Inc. Imprint: Dover Publications Inc. Dimensions: Width: 14.00cm , Height: 2.30cm , Length: 21.70cm Weight: 0.458kg ISBN: 9780486442372ISBN 10: 0486442373 Pages: 432 Publication Date: 13 May 2005 Audience: General/trade , General Format: Paperback Publisher's Status: Out of Stock Indefinitely Availability: In Print Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock. Table of ContentsPreface I. The Basic Concepts II. Desarguesian Spaces III. Perpendiculars and Parallels IV. Covering Spaces V. The Influence of the Sign of the Curvature on the Geodesics VI. Homogenous Spaces Appendix Notes to the Text IndexReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |