CR Hypersurfaces with a Contracting Automorphism
CR Hypersurfaces with a Contracting Automorphism
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具有收缩自同构的 CR 超曲面
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Sung
中科院分区：
文献类型：
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作者：
Kang;Sung
设M是n+1中的真实的解析CR超曲面，不允许正维数簇.我们首先证明了M的每一个收缩局部CR自同构都是可线性化的。因此，我们证明了允许收缩局部CR自同构的这样的M全纯等价于加权齐次超曲面。最后，我们应用这些结果证明了在n+1中具有真实的解析边界的有界域，若在边界点上有一个收缩的自同构，则在它的自同构群中必有一个真实的维数至少为2的李群.
Let M be a real analytic CR hypersurface in ℂn+1 admitting no varieties of positive dimension. We show first that every contracting local CR automorphism of M is linearizable. As a consequence, we show that such M admitting a contracting local CR automorphism is holomorphically equivalent to a weighted homogeneous hypersurface. Finally, we apply these results to prove that a bounded domain in ℂn+1 with a real analytic boundary admitting an automorphism contracting at a boundary point must admit a Lie subgroup of real dimension at least two in its automorphism group.