Journal for Geometry and Graphics 17 (2013), No. 2, 129--140
Copyright Heldermann Verlag 2013
Curve Flows on Ruled Surfaces
Markus Hagemann
Institut für Geometrie, Fachbereich Mathematik, Technische Universität, Zellescher Weg 12-14, 01069 Dresden, Germany
markus.hagemann@tu-dresden.de
Daniel Klawitter
Institut für Geometrie, Fachbereich Mathematik, Technische Universität, Zellescher Weg 12-14, 01069 Dresden, Germany
daniel.klawitter@tu-dresden.de
Boris Odehnal
Abteilung für Geometrie, Universität für Angewandte Kunst, Oskar-Kokoschka-Platz 2, 1010 Wien, Austria
boris.odehnal@uni-ak.ac.at
We study special flows of curves on ruled surfaces. Closed curves on closed ruled surfaces are driven by the Gaussian curvature flow and the geodesic curvature flow. For that we use a discretization of the ruled surfaces, the curves on them, and the curvatures. In an experimental part, the problem will be attacked numerically and various types of approximations will be used.
Keywords: Curve flow, curvature, geodesic flow, ruled surface, striction curve, geodesic curvature, Gaussian curvature.
MSC: 53A04; 53A05, 37E35
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