Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 2, pp. 489-503 (2006)
On boundary arcs joining antipodal points of a planar convex body
Gennadiy AverkovFaculty of Mathematics, University of Technology, D-09107 Chemnitz, Germany; e-mail: email@example.com
Abstract: Using notions of Minkowski geometry (i.e., of the geometry of finite dimenional Banach spaces) we find new characterizations of centrally symmetric convex bodies, equiframed curves, bodies of constant width and certain convex bodies with modified constant width property. In particular, we show that straightforward extensions of some properites of bodies of constant Euclidean width are also valid for bodies of constant Minkowskian width if the underlying Minkowskian circle is an equiframed curve. All obtained characterizations are restricted to the case of the plane and involve certain measures of boundary arcs that join antipodal points of a planar convex body.
Keywords: central symmetry, constant tangential width, constant width, equiframed curve, isoperimetrix, Minkowski plane, Minkowski space, Radon curve
Classification (MSC2000): 52A10, 52A38
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Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.