A new approach to differential geometry using Clifford's geometric algebra /
John Snygg.
- new york : springer science + business media ; 2012 .
- xvii, 465 pages : illustrations ; 24 cm.
Includes bibliographical references (pages 449-458) and index.
1. Introduction -- 2. Clifford algebra in Euclidean 3-space -- 3. Clifford algebra in Minkowski 4-space -- 4. Clifford algebra in flat n-space -- 5. Curved spaces -- 6. The Gauss-Bonnet formula -- 7. Some extrinsic geometry in En[superscript] -- 8. Non-Euclidean (hyperbolic) geometry -- 9. Ruled surfaces continued -- 10. Lines of curvature -- 11. Minimal surfaces -- 12. Some general relativity -- A.A matrix representation of a Clifford algebra -- B. Construction of matrix representations for dirac vectors -- C.A few terms of the Taylor's series for the urdī-copernican model for the outer planets -- D.A few terms of the Taylor's series for Kepler's orbits.