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Symmetry and the farthest point mapping on convex surfaces
-
Costin Vîlcu
and
Tudor Zamfirescu
Published/Copyright:
August 10, 2006
Abstract
Consider the mapping F associating to each point x of a convex surface the set of all points at maximal intrinsic distance from x. We provide a large class of surfaces on which F is single-valued and involutive. Moreover, we show that there are point-symmetric surfaces of revolution with F single-valued but not involutive.
Received: 2004-11-12
Published Online: 2006-08-10
Published in Print: 2006-07-01
© Walter de Gruyter
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Articles in the same Issue
- On the surjectivity of the canonical Gaussian map for multiple coverings
- A classification of 4-dimensional elation Laguerre planes of group dimension 10
- Completely regular ovals
- Symmetry and the farthest point mapping on convex surfaces
- Certain Roman and flock generalized quadrangles have nonisomorphic elation groups
- Similarity structures on the torus and the Klein bottle via triangulations
- On Euclidean designs
- Carnot spaces and the k-stein condition
- Simplicity of the universal quotient bundle restricted to congruences of lines in ℙ3
- Entropy of the geodesic flow for metric spaces and Bruhat–Tits buildings
