Differential Geometry

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.

Contenu

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