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Surfaces with congruent shadow-lines

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

CH. Charitos
CH. Charitos
Affiliation:
Department of Mathematics, University of Crete, Iraklion P.O. Box 470, Greece
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Extract

The aim of this paper is to prove the following

THEOREM. Let M be a C∞ compact and strictly convex surface embedded in the euclidean space E3 or in the hyperbolic space H3. We suppose that all shadow-lines ofM are congruent. Then M is a euclidean 2-sphere or a hyperbolic 2-sphere respectively.

MSC classification

Secondary: 52A15: Convex sets in $3$ dimensions (including convex surfaces)

Information

Type
Research Article
Information
Mathematika , Volume 37 , Issue 1 , June 1990 , pp. 43 - 58
Copyright
Copyright © University College London 1990

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References

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