Electronic Resource
Springer
Journal of geometry
56 (1996), S. 25-33
ISSN:
1420-8997
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The aim of this note is to investigate the behaviour of exterior and interior parallels at distanceε to a given convex body of constant width in the unitn-sphere. The boundaries of these bodies are 2-transnormal topological (n−1)-spheres. The range ofε is determined where these transnormal topological (n−1)-spheres bound convex bodies of constant width as well. In particular this leads to the following main result: LetC be a body of constant width (π/2)+x ε ((π/2), π) in the unit sphere Sn. ThenC contains a body C of constant width (π/2)−x such thatC is the closedx-neighborhood of C. Moreover, the bodyC is smooth.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01222680
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