Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 50, No. 2, pp. 369-387 (2009)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 2, pp. 369-387 (2009) |
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Conformal width in M{ö}bius geometryRémi Langevin and Eberhard TeufelUniversité de Bourgogne, Institut de Mathématiques de Bourgogne, CNRS Laboratory $\mbox{N}^{\circ}$ 5584, 21078 Dijon, France. e-mail: Remi.Langevin@u-bourgogne.fr; Universit{ä}t Stuttgart, Fakultät 8: Mathematik und Physik, Institut für Geometrie und Topologie, 70550 Stuttgart, Germanye-mail: Eberhard.Teufel@mathematik.uni-stuttgart.de Abstract: In this article we extend the euclidean concept of width to Möbius geometry. For pairs of curves in the plane or in the 2-sphere $S^2$ which are the two folds of an envelope of circles, the conformal width will be defined as the conformal distance between the osculating circles at corresponding points. We mainly study pairs of curves having constant conformal width. The main results characterize constant conformal width in terms of the geodesic curvature of the family of circles enveloping the pair of curves, seen as a curve in the 3-dimensional de Sitter space, and in terms of the conformal arc-lengths of the two folds of the envelope. Keywords: curves, conformal width, constant width, conformal 2-sphere, Möbius geometry Classification (MSC2000): 53A30, 53C40, 53A04 Full text of the article:
Electronic version published on: 28 Aug 2009. This page was last modified: 28 Jan 2013.
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