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Preprints from members of the UM School of Mathematics, September 2008 - present.
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Browsing Preprints by Author "Olver, Peter J."
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Item Differential invariants of maximally symmetric submanifolds(2008-09-16) Olver, Peter J.Let $G$ be a Lie group acting smoothly on a manifold $M$. A closed, nonsingular submanifold $S \subset M$ is called \is{maximally symmetric} if its symmetry subgroup $\sym S \subset G$ has the maximal possible dimension, namely $\dim \sym S = \dim S$, and hence $S = \sym S \cdot z_0$ is an orbit of $\sym S$. Maximally symmetric submanifolds are characterized by the property that all their differential invariants are constant. In this paper, we explain how to directly compute the numerical values of the differential invariants of a maximally symmetric submanifold from the infinitesimal generators of its symmetry group. The equivariant method of moving frames is applied to significantly simplify the resulting formulae. The method is illustrated by examples of curves and surfaces in various classical geometries.Item Lectures on moving frames(2009-01-21) Olver, Peter J.This article surveys the equivariant method of moving frames, along with a variety of applications to geometry, differential equations, computer vision, numerical analysis, the calculus of variations, and invariant curve flows.