The mathematical works of J. H. C. Whitehead. Volume I, Differential geometry / edited by I. M. James ; with a biographical note by M. H. A. Newman and Barbara Whitehead and a mathematical appreciation by John W. Milnor.

Format:

Book

Contributor:

James, I. M. (Ioan Mackenzie), 1928- editor.

Newman, M. H. A. (Maxwell Herman Alexander), 1897- contributor.

Whitehead, Barbara, contributor.

Milnor, John W. (John Willard), 1931- contributor.

Language:

English

Subjects (All):

Geometry, Differential.

Physical Description:

1 online resource (397 pages) : illustrations

Place of Publication:

Oxford : Pergamon Press, 1962.

Language Note:

English

Summary:

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

Contents:

Front Cover; Differential Geometry; Copyright Page; EDITORIAL PREFACE; ACKNOWLEDGMENT; Table of Contents; PUBLICATIONS OF J. H. C. WHITEHEAD; A BIOGRAPHICAL NOTE; THE WORK OF J. H. C. WHITEHEAD; 1. Geometry and Algebra; 2. Topology; CHAPTER 1. A THEOREM ON LINEAR CONNECTIONS; CHAPTER 2. ON LINEAR CONNECTIONS; CHAPTER 3. A METHOD OF OBTAINING NORMAL REPRESENTATIONS FOR A PROJECTIVE CONNECTION ; CHAPTER 4. ON A CLASS OF PROJECTIVELY FLAT AFFINE CONNECTIONS ; CHAPTER 5. THE REPRESENTATION OF PROJECTIVE SPACES; CHAPTER 6. A SET OF AXIOMS FOR DIFFERENTIAL GEOMETRY

CHAPTER 7. THE FOUNDATIONS OF DIFFERENTIAL GEOMETRY CHAPTER I.THE ARITHMETIC SPACE OF n DIMENSIONS; 1. Arithmetic points; 2. Linear dependence.; 3. Linear sub-spaces.; 4. Linear homogeneous transformations.; 5. Homogeneous linear equations.; 6. Translations.; 7. Flat sub-spaces.; 8. Non-homogeneous linear equations.; 9. Linear transformations.; 10. Affine theorems.; 11. We have seen that any linear transformation carries straight lines into straight lines.; 12. The elementary distance function.; CHAPTER II. GEOMETRIES, GROUPS AND COORDINATE SYSTEMS; 1. A Geometry as a Mathematical Science.

2. Transformation groups.3. Geometry and group-theory.; 4. An affine space.; 5. Affine spaces.; 6. Euclidean metric spaces.; 7. Euclidean geometry.; 8. Coordinate systems.; 9. A class of coordinate geometries.; 10. Centred affine geometry.; 11. Oriented Spaces.; 12. Oriented curves.; 13. Affine parameterizations.; 14. Projective and conformal geometry.; 15. Point transformations. Automorphisms.; 16. Changing views of geometry.; CHAPTER III. ALLOWABLE COORDINATES; 1. Functions of class u. ; 2. The implicit function theorem.; 3. Transformations of class u.; 4. Continuous transformations.

5. Pseudo-groups.6. n-cells of class u. ; 7. Simple manifolds of classu.; 8. Oriented simple manifolds.; 9. Allowable coordinate systems for a simple manifold.; 10. The differential equations of affine geometry.; 11. The differential equations of the straight lines.; 12. Integration of the differential equations of affine geometry.; 13. Three locally flat affine spaces.; 14. Geometric objects.; 15. Regular point transformations.; 16. Geometric objects and point transformations.; 17. Geometric objects and their geometries.; CHAPTER IV.CELLS AND SCALARS; 1. Purpose of the chapter.

2. k-cells in n-space.3. Implicit equations of ak-cell.; 4.Scalars.; 5. Sets of n - k scalars.; 6. Sets of scalars and oriented k-cells.; 7. k-spaces in the large.; 8. Local properties. Infinitesimal geometry.; 9. Equivalence of scalars.; CHAPTER V.TANGENT SPACES; 1. Differentials of a function.; 2. Transformations of differentials.; 3. Differentials at a point.; 4. Tangent spaces.; 5. Oriented tangent spaces.; 6. Approximate flatness near a given point.; 7. Differentials and k-cells.; 8. Geometry of the tangentspaces.; 9. Other coordinates in the tangentspaces; 10. Tangent and osculating Riemannian spaces.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on online resource; title from PDF title page (ebrary, viewed January 22, 2015).

ISBN:

1-4831-6473-X