Differential Geometry - 1st Edition - ISBN: 9780080098692, 9781483164731

Differential Geometry

1st Edition

The Mathematical Works of J. H. C. Whitehead

Editors: I. M. James
eBook ISBN: 9781483164731
Imprint: Pergamon
Published Date: 1st January 1962
Page Count: 396
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The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry contains all of Whitehead's published work on differential geometry, along with some papers on algebras. Most of these were written in the period 1929-1937, but a few later articles are included.
The book begins with a list of Whitehead's works, in chronological order of writing as well as a biographical note by M. H. A. Newman and Barbara Whitehead, and a mathematical appreciation by John Milnor. This is followed by separate chapters on topics such as linear connections; a method of obtaining normal representations for a projective connection; representation of projective spaces; convex regions in the geometry of paths; locally homogeneous spaces in differential geometry; and the decomposition of an infinitesimal group. Also included are chapters on locally homogeneous spaces in differential geometry; Maurer's equations; linear associative algebras; an expression of Hopf's invariant as an integral; and normalizators of transformation groups.

Table of Contents

Editorial Preface

Publications of J. H. C. Whitehead

A Biographical Note

The Work of J. H. C. Whitehead

A Theorem on Linear Connections

On Linear Connections

A Method of Obtaining Normal Representations for a Projective Connection

On a Class of Projectively Flat Affine Connections

The Representation of Projective Spaces

A Set of Axioms for Differential Geometry

The Foundations of Differential Geometry

Affine Spaces of Paths Which are Symmetric about Each Point

Convex Regions in the Geometry of Paths

Convex Regions in the Geometry of Paths - Addendum

The Weierstrass E-function in Differential Metric Geometry

On the Covering of a Complete Space by the Geodesics through a Point

Locally Homogeneous Spaces in Differential Geometry

Note on Maurer's Equations

On the Decomposition of an Infinitesimal Group

Certain Equations in the Algebra of a Semi-simple Infinitesimal Group

Note on Linear Associative Algebras

An Expression of Hopf's Invariant as an Integral

On Normalizators of Transformation Groups

Elie Joseph Cartan, 1869-1951

Contents of Volumes I to IV


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About the Editor

I. M. James

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