Differential invariants of conformal and projective surfaces (Q2473502)

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Differential invariants of conformal and projective surfaces
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    Differential invariants of conformal and projective surfaces (English)
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    27 February 2008
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    In the excellently written paper the authors investigate differential invariants of a generic surface in three-dimensional space for the conformal and the projective groups. As main results they show the following theorems: 1) Every differential invariant of a generic surface \(S\subset\mathbb{R}^3\) under the action of the conformal group \(\text{SO}(4,1)\) can be written in terms of a single third order invariant and its invariant derivatives. 2) Every differential invariant of a generic surface \(S\subset\mathbb{R}^3\) under the action of the projective group \(\text{PSL}(4)\) can be written in terms of a single fourth-order invariant and its invariant derivatives. The paper is completed by a lot of interesting and helpfull references.
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    conformal differential geometry
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    projective differential geometry
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    differential invariants
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    moving frame
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    syzygy
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    differential algebra
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