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

By John Snygg

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This comprehensive textbook simplifies the discussion of differential geometry to an accessible level by introducing Clifford algebra. It includes chapter-by-chapter exercises, and provides a rare undergraduate-level approach to the subject matter.

Full Description

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  • ISBN13: 978-0-8176-8282-8
  • 482 Pages
  • Publication Date: December 9, 2011
  • Available eBook Formats: PDF

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Full Description
Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates,  beginning-level graduate students, and researchers in the algebra and physics communities. 
Table of Contents

Table of Contents

  1. Preface.
  2. Introduction.
  3. Clifford Algebra in Euclidean 3
  4. Space.
  5. Clifford Algebra in Minkowski 4
  6. Space.
  7. Clifford Algebra in Flat n
  8. Space.
  9. Curved Spaces.
  10. The Gauss
  11. Bonnet Formula.
  12. Non
  13. Euclidean (Hyperbolic) Geometry.
  14. Some Extrinsic Geometry in E^n.
  15. Ruled Surfaces Continued.
  16. Lines of Curvature.
  17. Minimal Surfaces.
  18. Some General Relativity.
  19. Matrix Representation of a Clifford Algebra.
  20. Construction of Coordinate Dirac Matrices.
  21. A Few Terms of the Taylor's Series for the Urdī
  22. Copernican Model for the Outer Planets.
  23. A Few Terms of the Taylor's Series for Kepler's Orbits.
  24. References.
  25. Index.

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