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Intrinsic Differential Geometry with Geometric Calculus

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Computer Algebra and Geometric Algebra with Applications (IWMM 2004, GIAE 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3519))

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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.

Supported partially by NKBRSF 2004CB318001 and NSFC 10471143.

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References

  1. Chern, S.S., Chen, W.-H., Lan, K.-S.: Lectures on Differential Geometry. World Scientific, Singapore (1999)

    MATH  Google Scholar 

  2. Hestenes, D., Sobczyk, G.: Clifford Algebra to Geometric Calculus. D. Reidel, Dordrecht (1984)

    MATH  Google Scholar 

  3. Li, H.: In: Proc. ASCM 1995, pp. 29–32. Scientists Inc, Tokyo (1995)

    Google Scholar 

  4. Li, H.: On mechanical theorem proving in differential geometry – local theory of surfaces. Science in China A 40(4), 350–356 (1997)

    Article  MATH  Google Scholar 

  5. Li, H.: Mechanical theorem proving in differential geometry. In: Gao, X.-S., Wang, D. (eds.) Mathematics Mechanization and Applications, pp. 147–174. Academic Press, London (2000)

    Google Scholar 

  6. Willmore, T.J.: Riemannian Geometry. Clarendon Press, Oxford (1993)

    MATH  Google Scholar 

  7. Wu, W.-T.: On the mechanization of theorem-proving in elementary differential geometry. Scientia Sinica (Math. Suppl. I), 94–102 (1979)

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China

    Hongbo Li, Lina Cao, Nanbin Cao & Weikun Sun

Authors
  1. Hongbo Li
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  2. Lina Cao
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  3. Nanbin Cao
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  4. Weikun Sun
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Editor information

Editors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, CAS, P.O. Box, 100080, Beijing, P.R. China

    Hongbo Li

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, U.S.A.

    Peter J. Olver

  3. Institute of Computer Science, Christian-Albrecht-University, 24098, Kiel, Germany

    Gerald Sommer

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© 2005 Springer-Verlag Berlin Heidelberg

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Li, H., Cao, L., Cao, N., Sun, W. (2005). Intrinsic Differential Geometry with Geometric Calculus. In: Li, H., Olver, P.J., Sommer, G. (eds) Computer Algebra and Geometric Algebra with Applications. IWMM GIAE 2004 2004. Lecture Notes in Computer Science, vol 3519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499251_17

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  • DOI: https://doi.org/10.1007/11499251_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26296-1

  • Online ISBN: 978-3-540-32119-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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