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In this paper, we prove that the automorphism group of a quasi-homogeneous properly convex affine domain in $\mathbb R^n$ acts transitively on the set of all the extreme points of the domain. This set is equal to the set of all the asymptotic cone points coming from the asymptotic foliation of the domain and thus it is a homogeneous submanifold of $\mathbb R^n$.
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참고문헌 (4)
참고문헌 신청
J. P. Benzecri / 1960 / Sur les varietes localement affines et projectives / Bull. Soc. Math. France 88 : 229 ~ 332
J. Vey / 1970 / Sur les automorphismes affines des ouverts convexes saillants / Ann. Scuola Norm. Sup. Pisa 24 (3) : 641 ~ 665
K. Jo / 2003 / Quasi-homogeneous domains and convex affine manifolds / Topology Appl 134 (2) : 123 ~ 146
Kyeonghee Jo / 2005 / DIFFERENTIABILITY OF QUASI- HOMOGENEOUS CONVEX AFFINE DOMAINS / 대한수학회지 42 (3) : 485 ~ 498
J. Vey / 1970 / Sur les automorphismes affines des ouverts convexes saillants / Ann. Scuola Norm. Sup. Pisa 24 (3) : 641 ~ 665
K. Jo / 2003 / Quasi-homogeneous domains and convex affine manifolds / Topology Appl 134 (2) : 123 ~ 146
Kyeonghee Jo / 2005 / DIFFERENTIABILITY OF QUASI- HOMOGENEOUS CONVEX AFFINE DOMAINS / 대한수학회지 42 (3) : 485 ~ 498
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