Moving Coframes: I. A Practical Algorithm

Mark Fels, Peter J. Olver

Research output: Contribution to journalArticlepeer-review

170 Scopus citations

Abstract

This is the first in a series of papers devoted to the development and applications of a new general theory of moving frames. In this paper, we formulate a practical and easy to implement explicit method to compute moving frames, invariant differential forms, differential invariants and invariant differential operators, and solve general equivalence problems for both finite-dimensional Lie group actions and infinite Lie pseudo-groups. A wide variety of applications, ranging from differential equations to differential geometry to computer vision are presented. The theoretical justifications for the moving coframe algorithm will appear in the next paper in this series.

Original languageEnglish (US)
Pages (from-to)161-213
Number of pages53
JournalActa Applicandae Mathematicae
Volume51
Issue number2
DOIs
StatePublished - 1998

Bibliographical note

Funding Information:
★ Supported in part by an NSERC Postdoctoral Fellowship. Supported in part by NSF Grant DMS 95-00931.

Keywords

  • Computer vision
  • Differential invariant
  • Equivalence
  • Lie group
  • Lie pseudogroup
  • Moving frame
  • Symmetry

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