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Geometric Poisson brackets on Grassmannians and conformal spheres

Eastwood, Michael; Beffa, Mari


We relate the geometric Poisson brackets on the 2-Grassmannian in4 and on the (2, 2) Mbius sphere. We show that, when written in terms of local moving frames, the geometric Poisson bracket on the Mbius sphere does not restrict to the space of differential invariants of Schwarzian type. But when the concept of conformal natural frame is transported from the conformal sphere into the Grassmannian, and the Poisson bracket is written in terms of the Grassmannian natural frame, it restricts and...[Show more]

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
Source: Proceedings of the Royal Society of Edinburgh
DOI: 10.1017/S0308210510001071
Access Rights: Open Access


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