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Inductive Moving Frames

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Abstract

An inductive implementation of the equivariant moving frame method is introduced for both finite-dimensional Lie group actions and infinite-dimensional Lie pseudo-groups. Given two Lie (pseudo-)groups \({\mathcal{G}}\) and \({\mathcal{H}}\) with \({\mathcal{G} \subset \mathcal{H}}\), the inductive method streamlines the construction of a moving frame for \({\mathcal{H}}\) using the already constructed moving frame for \({\mathcal{G}}\). As a by-product, a systematic procedure for expressing \({\mathcal{H}}\)-invariant quantities in terms of their \({\mathcal{G}}\)-invariant counterparts is obtained.

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  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada

    Francis Valiquette

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  1. Francis Valiquette
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Correspondence to Francis Valiquette.

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Supported by an AARMS Postdoctoral Fellowship.

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Valiquette, F. Inductive Moving Frames. Results. Math. 64, 37–58 (2013). https://doi.org/10.1007/s00025-012-0294-2

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  • DOI: https://doi.org/10.1007/s00025-012-0294-2

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