Proceedings of the Japan Academy, Series A, Mathematical Sciences

The gradient maps associated to certain non-homogeneous cones

Hideyuki Ishi

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The gradient map associated to a regular open convex cone gives a diffeomorphism from the cone onto its dual cone. If the cone is homogeneous, the inverse of the map is known to be equal to the gradient map associated to the dual cone. However, we show that this is no longer true for a general case by presenting a simple counterexample.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 3 (2005), 44-46.

First available in Project Euclid: 18 May 2005

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Primary: 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 53A15: Affine differential geometry 52A15: Convex sets in 3 dimensions (including convex surfaces) [See also 53A05, 53C45]

Regular open convex cone dual cone gradient map


Ishi, Hideyuki. The gradient maps associated to certain non-homogeneous cones. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 3, 44--46. doi:10.3792/pjaa.81.44.

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