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

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 ta...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Snygg, John (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
Edición:1st ed. 2012.
Temas:
Geometry, Differential.
Mathematical physics.
Mathematics.
Algebra.
Differential Geometry.
Mathematical Methods in Physics.
Mathematical Physics.
Applications of Mathematics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Preface
  • Introduction
  • Clifford Algebra in Euclidean 3-Space
  • Clifford Algebra in Minkowski 4-Space
  • Clifford Algebra in Flat n-Space
  • Curved Spaces
  • The Gauss-Bonnet Formula
  • Non-Euclidean (Hyperbolic) Geometry
  • Some Extrinsic Geometry in E^n
  • Ruled Surfaces Continued
  • Lines of Curvature
  • Minimal Surfaces
  • Some General Relativity
  • Matrix Representation of a Clifford Algebra
  • Construction of Coordinate Dirac Matrices
  • A Few Terms of the Taylor's Series for the Urdī-Copernican Model for the Outer Planets
  • A Few Terms of the Taylor's Series for Kepler's Orbits
  • References
  • Index.

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