A characterization of centrally symmetric convex bodies in terms of visual cones
-
E. Morales-Amaya
and
D. J. Verdusco Hernández
Abstract
We prove the following result: Let K be a strictly convex body in the Euclidean space ℝn, n ≥ 3, and let L be a hypersurface which is the image of an embedding of the sphere 𝕊n–1, such that K is contained in the interior of L. Suppose that, for every x ∈ L, there exists y ∈ L such that the support cones of K with apexes at x and y differ by a central symmetry. Then K and L are centrally symmetric and concentric.
Acknowledgements
We thank the anonymous referee for his/her valuable comments and corrections which improve the readability of the paper.
Communicated by: M. Henk
References
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Articles in the same Issue
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- On weak Fano manifolds with small contractions obtained by blow-ups of a product of projective spaces
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- Positive semigroups in lattices and totally real number fields
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Articles in the same Issue
- Frontmatter
- On weak Fano manifolds with small contractions obtained by blow-ups of a product of projective spaces
-
A geographical study of
- A characterization of centrally symmetric convex bodies in terms of visual cones
- Closed Majorana representations of {3, 4}+-transposition groups
- Real hypersurfaces in ℂP2 and ℂH2 with constant scalar curvature
- Positive semigroups in lattices and totally real number fields
- A new axiomatics for masures II
- Helmut Salzmann and his legacy
- Some remarks on proper actions, proper metric spaces, and buildings
- Regular parallelisms on PG(3,ℝ) from generalized line stars: the oriented case
- A note on the Kleinewillinghöfer types of 4-dimensional Laguerre planes
- Sixteen-dimensional compact translation planes with automorphism groups of dimension at least 35
