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Symmetric homogeneous convex domains

Published online by Cambridge University Press:  22 January 2016

Tadashi Tsuji
Tadashi Tsuji*
Affiliation:
Department of Mathematics, Mie University, Tsu, Mie 514, Japan
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Let D be a convex domain in the n-dimensional real number space Rn, not containing any affine line and A(D) the group of all affine transformations of Rn leaving D invariant. If the group A(D) acts transitively on D, then the domain D is said to be homogeneous. From a homogeneous convex domain D in Rn, a homogeneous convex cone V = V(D) in Rn+1 = Rn × R is constructed as follows (cf. Vinberg [11]):

which is called the cone fitted on the convex domain D.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 93 , March 1984 , pp. 1 - 17
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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