• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.859-867
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• 2002

In this paper, we get a necessary and sufficient condition for an inner automorphism between compact connected semisimple Lie groups to be an atone transformation, and obtain atone transformations of (SU(n),g) with some left invariant metric g.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.643-652
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• 2022

In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1221-1241
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• 2008

Most of domains people have studied are convex bounded projective (or affine) domains. Edith $Soci{\acute{e}}$-$M{\acute{e}}thou$ [15] characterized ellipsoid in ${\mathbb{R}}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.