논문KCI 등재
Asymptotic foliations of quasi-homogeneous convex affine domains
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회논문집 (Communications of the KMS)|제32권 제1호|pp. 165-173
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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 $\mathbb R^n$.
Abstract
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 $\mathbb R^n$.
참고문헌 (4)
- J. P. Benzécri, "Sur les variétés localement affines et projectives", Bull. Soc. Math. France, 88, pp.229~332 (1960)
- K. Jo, "Quasi-homogeneous domains and convex affine manifolds", Topology Appl, 134(2), pp.123~146 (2003)
- Kyeonghee Jo, "DIFFERENTIABILITY OF QUASI- HOMOGENEOUS CONVEX AFFINE DOMAINS", 대한수학회지, 42(3), pp.485~498 (2005), 대한수학회
- J. Vey, "Sur les automorphismes affines des ouverts convexes saillants", Ann. Scuola Norm. Sup. Pisa, 24(3), pp.641~665 (1970)
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