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

Front Cover
Springer Science & Business Media, Dec 8, 2011 - Mathematics - 465 pages
0 Reviews

Differential geometry is the study of the curvature and calculus of curves and surfaces. The conceptual complications introduced by a multitude of spaces and mappings normally required in the study of differential geometry usually postpones the topic to graduate-level courses. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an undergraduate level of differential geometry by introducing Clifford algebra. This presentation is relevant since Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.

Key features include:

· a rare undergraduate-level approach to differential geometry;

· brief biographies of historically relevant mathematicians and physicists;

· significant aspects of general relativity and Riemannian geometry and

· chapter-by-chapter exercises.

This accessible and comprehensive textbook offers a valuable introduction to differential geometry, simplifying the complicated theory by using Clifford algebra. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

This accessible and comprehensive textbook offers a valuable introduction to differential geometry, simplifying the complicated theory by using Clifford algebra. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Chapter 1 Introduction
1
Chapter 2 Clifford Algebra in Euclidean 3Space
3
Chapter 3 Clifford Algebra in Minkowski 4Space
27
Chapter 4 Clifford Algebra in Flat nSpace
47
Chapter 5 Curved Spaces
121
Chapter 6 The GaussBonnet Formula
181
Chapter 7 Some Extrinsic Geometry in En
227
Chapter 8 NonEuclidean Hyperbolic Geometry
299
Chapter 11 Minimal Surfaces
375
Chapter 12 Some General Relativity
395
Chapter A A Matrix Representation of a Clifford Algebra
431
Chapter B Construction of Matrix Representations for Dirac Vectors
436
Chapter C A Few Terms of the Taylors Series for the UrdıCopernican Model for the Outer Planets
441
Chapter D A Few Terms of the Taylors Series for Keplers Orbits
444
References
449
Index
459

Chapter 9 Ruled Surfaces Continued
333
Chapter 10 Lines of Curvature
347

Other editions - View all

Common terms and phrases

Bibliographic information