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.
For the entire collection see [Zbl 1048.53002].


53A05 Surfaces in Euclidean and related spaces
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
53A55 Differential invariants (local theory), geometric objects
65D17 Computer-aided design (modeling of curves and surfaces)
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
53A04 Curves in Euclidean and related spaces


moving frames
Full Text: EMIS