The Geometry of Geodesics

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book The Geometry of Geodesics by Herbert Busemann, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Herbert Busemann ISBN: 9780486154626
Publisher: Dover Publications Publication: July 12, 2012
Imprint: Dover Publications Language: English
Author: Herbert Busemann
ISBN: 9780486154626
Publisher: Dover Publications
Publication: July 12, 2012
Imprint: Dover Publications
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Dover Publications

Cover of the book Pawn Power in Chess by Herbert Busemann
Cover of the book Flowers of Evil and Other Works by Herbert Busemann
Cover of the book Great Ghost Stories by Herbert Busemann
Cover of the book Smaller Houses of the 1920s by Herbert Busemann
Cover of the book 2,001 Most Useful Spanish Words by Herbert Busemann
Cover of the book Vivid and Repulsive as the Truth by Herbert Busemann
Cover of the book Computability and Unsolvability by Herbert Busemann
Cover of the book A Shakespearian Grammar by Herbert Busemann
Cover of the book Handbook of Historic Ornament by Herbert Busemann
Cover of the book James Joyce The Dover Reader by Herbert Busemann
Cover of the book The Tale of Frisky Squirrel by Herbert Busemann
Cover of the book North American Indian Beadwork Designs by Herbert Busemann
Cover of the book A Little Princess by Herbert Busemann
Cover of the book Those Were the Days: Weird and Wacky Ads of Yesteryear by Herbert Busemann
Cover of the book Robust Adaptive Control by Herbert Busemann
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy