A new approach to differential geometry using Clifford's geometric algebra

Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's GeometricAlgebra 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. Includes chapter-by-chapter exercises. Provides a rare undergraduate-level approach to the subject matter. Promotes the application of Clifford algebra to differential geometry. Presents a significant portion of general relativity without reference to such Newtonian terms as 'force', 'momentum', or 'energy'. Only up-to-date title of its kind. INDICE: 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 Seriesfor the Urd?-Copernican Model for the Outer Planets. A Few Terms of the Taylor's Series for Kepler's Orbits. References. Index.

• ISBN: 978-0-8176-8282-8
• Editorial: Birkhäuser Boston
• Encuadernacion: Cartoné
• Páginas: 465
• Fecha Publicación: 28/11/2011
• Nº Volúmenes: 1
• Idioma: Inglés