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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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.
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Book Description Academic Press, New York, 1955. hardcover. Book Condition: Fair. N/A. Former Library book. Shows definite wear, and perhaps considerable marking on inside. Bookseller Inventory # GRP91161463
Book Description Academic Pr, 1996. Hardcover. Book Condition: Used: Good. We ship International with Tracking Number! May not contain Access Codes or Supplements. Buy with confidence, excellent customer service! j. Bookseller Inventory # 0121483509D