Proceedings of the Japan Academy, Series A, Mathematical Sciences

A characterization of convex cones

Kyeonghee Jo

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Any convex cone has an accumulation point in the base by the action of its automorphism group. In this paper, we prove the converse of this statement, more precisely, a convex domain $\Omega$ with a face $F$ of codimension 1 is a cone over $F$ if there is an Aut($\Omega$)-orbit accumulating at a point of $F$.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 84, Number 10 (2008), 175-178.

First available in Project Euclid: 2 December 2008

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Zentralblatt MATH identifier

Primary: 57S20: Noncompact Lie groups of transformations 57N16: Geometric structures on manifolds [See also 57M50] 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 32F45: Invariant metrics and pseudodistances

Cone convex domain projective transformation


Jo, Kyeonghee. A characterization of convex cones. Proc. Japan Acad. Ser. A Math. Sci. 84 (2008), no. 10, 175--178. doi:10.3792/pjaa.84.175.

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