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Intrinsic Differential Geometry with Geometric Calculus

  • Hongbo Li
  • Lina Cao
  • Nanbin Cao
  • Weikun Sun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3519)

Abstract

Setting up a symbolic algebraic system is the first step in mathematics mechanization of any branch of mathematics. In this paper, we establish a compact symbolic algebraic framework for local geometric computing in intrinsic differential geometry, by choosing only the Lie derivative and the covariant derivative as basic local differential operators. In this framework, not only geometric entities such as the curvature and torsion of an affine connection have elegant representations, but their involved local geometric computing can be simplified.

Keywords

Intrinsic differential geometry Clifford algebra Mathematics mechanization Symbolic geometric computing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hongbo Li
    • 1
  • Lina Cao
    • 1
  • Nanbin Cao
    • 1
  • Weikun Sun
    • 1
  1. 1.Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingP. R. China

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