The gradient maps associated to certain non-homogeneous cones
Hideyuki Ishi
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 81, Number 3
(2005), 44-46.
Abstract
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.
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Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442035
Mathematical Reviews number (MathSciNet): MR2128930
Zentralblatt MATH identifier: 1086.52501
Digital Object Identifier: doi:10.3792/pjaa.81.44
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Proceedings of the Japan Academy, Series A, Mathematical Sciences
