eBook - ePub

The Geometry of Geodesics

Name: The Geometry of Geodesics
ISBN: 9780486154626

Herbert Busemann,

432 pages
English
ePUB (mobile friendly)
Available on iOS & Android

eBook - ePub

The Geometry of Geodesics

Herbert Busemann,

About this book

A 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.

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Yes, you can access The Geometry of Geodesics by Herbert Busemann in PDF and/or ePUB format, as well as other popular books in Mathematics & Geometry. We have over one million books available in our catalogue for you to explore.