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

✍ Scribed by John Snygg (auth.)

• Publisher: Birkhäuser Basel
• Year: 2012
• Tongue: English
• Leaves: 484
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xvii
Introduction....Pages 1-2
Clifford Algebra in Euclidean 3-Space....Pages 3-25
Clifford Algebra in Minkowski 4-Space....Pages 27-46
Clifford Algebra in Flat n-Space....Pages 47-120
Curved Spaces....Pages 121-179
The Gauss–Bonnet Formula....Pages 181-226
Some Extrinsic Geometry in E n ....Pages 227-298
Non-Euclidean (Hyperbolic) Geometry....Pages 299-331
Ruled Surfaces Continued....Pages 333-345
Lines of Curvature....Pages 347-373
Minimal Surfaces....Pages 375-394
Some General Relativity....Pages 395-430
Back Matter....Pages 431-465

✦ Subjects

Differential Geometry;Mathematical Methods in Physics;Mathematical Physics;Mathematics, general;Algebra;Applications of Mathematics