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Uniqueness theorems for convex bodies in non-Euclidean spaces

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Paolo Dulio  and
Carla Peri
Paolo Dulio
Affiliation:
Dipartimento di Matematica “F. Brioschi”, Politeenico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano E-mail:paodul@mate.polimi.it
Carla Peri
Affiliation:
Università Cattolica S.C., Largo Gemelli 1, I-20123 Milano E-mail:carla.peri@unicatt.it
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Abstract

The notion of generalized X-ray for star sets in a Riemannian manifold is introduced to prove uniqueness theorems for convex bodies contained in a simply convex neighbourhood of a two-manifold. These results extend to the whole space and to arbitrary dimension when spaces of constant curvature are considered. As a consequence, a characterization of centrally symmetric convex bodies is obtained.

MSC classification

Secondary: 52A55: Spherical and hyperbolic convexity
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 13 - 31
Copyright
Copyright © University College London 2002

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