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
Chern, S.S., Chen, W.-H., Lan, K.-S.: Lectures on Differential Geometry. World Scientific, Singapore (1999)
Hestenes, D., Sobczyk, G.: Clifford Algebra to Geometric Calculus. D. Reidel, Dordrecht (1984)
Li, H.: In: Proc. ASCM 1995, pp. 29–32. Scientists Inc, Tokyo (1995)
Li, H.: On mechanical theorem proving in differential geometry – local theory of surfaces. Science in China A 40(4), 350–356 (1997)
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)
Willmore, T.J.: Riemannian Geometry. Clarendon Press, Oxford (1993)
Wu, W.-T.: On the mechanization of theorem-proving in elementary differential geometry. Scientia Sinica (Math. Suppl. I), 94–102 (1979)
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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
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