Sinossi
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.
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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Product Description
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text opens with an explanation of the basic concepts and proceeds to discussions of Desarguesian spaces, perpendiculars and parallels, and covering spaces. Concluding chapters examine the influence of the sign of the curvature on geodesics and homogenous spaces. 1955 edition. Includes 66 figures.
Contenuti
Preface 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 Index
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The Geometry of Geodesics (Dover Books on Mathematics)
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Dover Publications, 2005
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The Geometry of Geodesics (Dover Books on Mathematics)
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