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Centroaffine translation surfaces in \(\mathbb{R}^3\) - MaRDI portal

Centroaffine translation surfaces in \(\mathbb{R}^3\) (Q2655722)

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Centroaffine translation surfaces in \(\mathbb{R}^3\)
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    Centroaffine translation surfaces in \(\mathbb{R}^3\) (English)
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    26 January 2010
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    As the attempt to classify centroaffine surfaces with constant Gauss curvature failed due to the abundance of solutions, the authors restrict to translation surfaces in \(\mathbb R^3\). In this paper they explicitly classify the centroaffine translation surfaces a) with constant Gauss curvature \(K\), b) with constant Pick invariant \(J\) and c) with constant \(K-J\) or-equivalently-constant absolute value of the Tchebycheff vector field \(T\).
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    centroaffine differential geometry
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    translation surface
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    Gauss curvature
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    Pick invariant
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