A New Approach to Differential Geometry using Clifford's Geometric Algebra

  • John Snygg

Table of contents

  1. Front Matter
    Pages i-xvii
  2. John Snygg
    Pages 1-2
  3. John Snygg
    Pages 27-46
  4. John Snygg
    Pages 47-120
  5. John Snygg
    Pages 121-179
  6. John Snygg
    Pages 181-226
  7. John Snygg
    Pages 227-298
  8. John Snygg
    Pages 299-331
  9. John Snygg
    Pages 333-345
  10. John Snygg
    Pages 347-373
  11. John Snygg
    Pages 375-394
  12. John Snygg
    Pages 395-430
  13. Back Matter
    Pages 431-465

About this book

Introduction

Differential geometry is the study of curvature and calculus of curves and surfaces.  Because of an historical accident, the Geometric Algebra devised by William Kingdom Clifford (1845–1879) has been overlooked in favor of the more complicated and less powerful formalism of differential forms and tangent vectors to deal with differential geometry.  Fortuitously a student who has completed an undergraduate course in linear algebra is better prepared to deal with the intricacies of Clifford algebra than with the formalism currently used.  Clifford algebra enables one to demonstrate a close relation between curvature and certain rotations.  This is an advantage both conceptually and computationally—particularly in higher dimensions.

Key features and topics include:

* a unique undergraduate-level approach to differential geometry;

* brief biographies of historically relevant mathematicians and physicists;

* some aspects of special and general relativity accessible to undergraduates with no knowledge of Newtonian physics;

* chapter-by-chapter exercises.

The textbook will also serve as a useful classroom resource primarily for undergraduates as well as beginning-level graduate students; researchers in the algebra and physics communities may also find the book useful as a self-study guide.

Keywords

Clifford algebra Gauss-Bonnet formula Taylor's series curved spaces differential geometry general relativity non-Euclidean geometry

Authors and affiliations

  • John Snygg
    • 1
  1. 1.East OrangeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8283-5
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8282-8
  • Online ISBN 978-0-8176-8283-5
  • About this book