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On Zindler Curves in Normed Planes

  Published:2011-06-08
 Printed: Dec 2012
  • Horst Martini,
    Faculty of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany
  • Senlin Wu,
    Department of Applied Mathematics, Harbin University of Science and Technology, 150080 Harbin, China
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Abstract

We extend the notion of Zindler curve from the Euclidean plane to normed planes. A characterization of Zindler curves for general normed planes is given, and the relation between Zindler curves and curves of constant area-halving distances in such planes is discussed.
Keywords: rc length, area-halving distance, Birkhoff orthogonality, convex curve, halving pair, halving distance, isosceles orthogonality, midpoint curve, Minkowski plane, normed plane, Zindler curve rc length, area-halving distance, Birkhoff orthogonality, convex curve, halving pair, halving distance, isosceles orthogonality, midpoint curve, Minkowski plane, normed plane, Zindler curve
MSC Classifications: 52A21, 52A10, 46C15 show english descriptions Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
Convex sets in $2$ dimensions (including convex curves) [See also 53A04]
Characterizations of Hilbert spaces
52A21 - Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
52A10 - Convex sets in $2$ dimensions (including convex curves) [See also 53A04]
46C15 - Characterizations of Hilbert spaces
 

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