Herbert Busemann's Books

The Geometry of Geodesics

By: Herbert Busemann

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A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.

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Page Count

434

Publisher

Courier Corporation

Published Date

ISBN 10

0486154629

ISBN 13

9780486154626

Projective Geometry and Projective Metrics

By: Herbert Busemann,Paul J. Kelly

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Projective Geometry and Projective Metrics

By: Herbert Busemann,Paul J. Kelly

This text examines the 3 classical geometries and their relationship to general geometric structures, with particular focus on affine geometry, projective metrics, non-Euclidean geometry, and spatial geometry. 1953 edition.

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Page Count

350

Publisher

Courier Corporation

Published Date

ISBN 10

0486154696

ISBN 13

9780486154695

Recent Synthetic Differential Geometry

By: Herbert Busemann

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Recent Synthetic Differential Geometry

By: Herbert Busemann

A synthetic approach to intrinsic differential geometry in the large and its connections with the foundations of geometry was presented in "The Geometry of Geodesics" (1955, quoted as G). It is the purpose of the present report to bring this theory up to date. Many of the later ip.vestigations were stimulated by problems posed in G, others concern newtopics. Naturally references to G are frequent. However, large parts, in particular Chapters I and III as weIl as several individual seetions, use only the basic definitions. These are repeated here, sometimes in a slightly different form, so as to apply to more general situations. In many cases a quoted result is quite familiar in Riemannian Geometry and consulting G will not be found necessary. There are two exceptions : The theory of paralleIs is used in Sections 13, 15 and 17 without reformulating all definitions and properties (of co-rays and limit spheres). Secondly, many items from the literature in G (pp. 409-412) are used here and it seemed superfluous to include them in the present list of references (pp. 106-110). The quotations are distinguished by [ ] and ( ), so that, for example, FreudenthaI [1] and (I) are found, respectively, in G and here.

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Page Count

119

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642880576

ISBN 13

9783642880575

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

By: Herbert Busemann

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Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

By: Herbert Busemann

The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.

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Page Count

243

Publisher

Princeton University Press

Published Date

ISBN 10

140088229X

ISBN 13

9781400882298

Finite Sections of Some Classical Inequalities

By: Herbert S. Wilf

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Finite Sections of Some Classical Inequalities

By: Herbert S. Wilf

Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. This family of inequalities determines the best bound of a family of operators on /p. When such inequalities are restricted only to finitely many variables, we can then ask for the rate at which the bounds of the restrictions approach the uniform bound. In the context of Toeplitz forms, such research was initiated over fifty years ago by Szego [37J, and the chain of ideas continues to grow strongly today, with fundamental contributions having been made by Kac, Widom, de Bruijn, and many others. In this monograph I attempt to draw together these lines of research from the point of view of sharpenings of the classical inequalities of [17]. This viewpoint leads to the exclusion of some material which might belong to a broader-based discussion, such as the elegant work of Baxter, Hirschman and others on the strong Szego limit theorem, and the inclusion of other work, such as that of de Bruijn and his students, which is basically nonlinear, and is therefore in some sense disjoint from the earlier investigations. I am grateful to Professor Halmos for inviting me to prepare this volume, and to Professors John and Olga Todd for several helpful comments. Philadelphia, Pa. H.S.W.

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Springer Science & Business Media

Published Date

ISBN 10

364286712X

ISBN 13

9783642867125

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

By: Herbert Busemann

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Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

By: Herbert Busemann

The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.

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Solve jigsaw puzzle

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243

Publisher

Princeton University Press

Published Date

ISBN 10

140088229X

ISBN 13

9781400882298

Book's by Herbert Busemann

The Geometry of Geodesics

The Geometry of Geodesics

Projective Geometry and Projective Metrics

Projective Geometry and Projective Metrics

Recent Synthetic Differential Geometry

Recent Synthetic Differential Geometry

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

Finite Sections of Some Classical Inequalities

Finite Sections of Some Classical Inequalities

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

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