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 A Study in Scarlet and The Sign of Four by Herbert Busemann
Cover of the book The Specificity of Serological Reactions by Herbert Busemann
Cover of the book Applied Group Theory by Herbert Busemann
Cover of the book The Traffic Assignment Problem by Herbert Busemann
Cover of the book Life of Black Hawk by Herbert Busemann
Cover of the book English Fairy Tales by Herbert Busemann
Cover of the book Introduction to Proof in Abstract Mathematics by Herbert Busemann
Cover of the book American Victorian Costume in Early Photographs by Herbert Busemann
Cover of the book The Fabric of Dreams by Herbert Busemann
Cover of the book None But the Lonely Heart and Other Songs for High Voice by Herbert Busemann
Cover of the book Whittling and Woodcarving by Herbert Busemann
Cover of the book Poor Richard's Almanack and Other Writings by Herbert Busemann
Cover of the book A Glossary of the Construction, Decoration and Use of Arms and Armor by Herbert Busemann
Cover of the book Short Stories by Herbert Busemann
Cover of the book A Treasury of Biblical Quotations 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