Differential Geometry

The Mathematical Works of J. H. C. Whitehead

I. M. James

• Publisher: Pergamon
• Year: 2014
• Print ISBN:
  9780080098692
• eBook ISBN:
  9781483164731
• Topic: Mathematics
• Subtopic: Differential Geometry
• Index: Mathematics

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

• Front Cover
• Differential Geometry
• Copyright Page
• Table of Contents
• EDITORIAL PREFACE
• ACKNOWLEDGMENT
• PUBLICATIONS OF J. H. C. WHITEHEAD
• A BIOGRAPHICAL NOTE
• THE WORK OF J. H. C. WHITEHEAD
• 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 8. AFFINE SPACES OF PATHS WHICH ARE SYMMETRIC ABOUT EACH POINT
• CHAPTER 9. CONVEX REGIONS IN THE GEOMETRY OF PATHS
• CHAPTER 10. CONVEX REGIONS IN THE GEOMETRY OF PATHS—ADDENDUM
• CHAPTER 11. THE WEIERSTRASS E-FUNCTION IN DIFFERENTIAL METRIC GEOMETRY
• CHAPTER 12. ON THE COVERING OF A COMPLETE SPACE BY THE GEODESICS THROUGH A POINT
• CHAPTER 13. LOCALLY HOMOGENEOUS SPACES IN DIFFERENTIAL GEOMETRY
• CHAPTER 14. NOTE ON MAURER'S EQUATIONS
• CHAPTER 15. ON THE DECOMPOSITION OF AN INFINITESIMAL GROUP
• CHAPTER 16. CERTAIN EQUATIONS IN THE ALGEBRA OF A SEMI-SIMPLE INFINITESIMAL GROUP
• CHAPTER 17. NOTE ON LINEAR ASSOCIATIVE ALGEBRAS
• CHAPTER 18. AN EXPRESSION OF HOPF'S INVARIANT AS AN INTEGRAL
• CHAPTER 19. ON NORMALIZATORS OF TRANSFORMATION GROUPS
• CHAPTER 20. ELIE JOSEPH CARTAN
• CONTENTS OF VOLUMES I TO IV