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An introduction to moving frames. (English) Zbl 1069.53005
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5–12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 67-80 (2004).
Since the method of moving frames was introduced by G. Darboux and developed by E. Cartan it has become a powerful tool for discussing geometric properties of submanifolds with respect to a transformation group in differential geometry. A new approach to moving frames, defining them as equivariant maps from the manifold M to the Lie group acting on M is due to the author. The present paper is a good survey of one of the main contributors to the theory of moving frames indicating applications in geometry, computer vision, classical invariant theory and numerical analysis.
MSC:
53A05Surfaces in Euclidean space
53-02Research monographs (differential geometry)
53A55Differential invariants (local theory), geometric objects
65D17Computer aided design (modeling of curves and surfaces)
68U05Computer graphics; computational geometry
53A04Curves in Euclidean space
Keywords:
moving frames