Existence of Real Analytic Surfaces with Hyperbolic Complex Tangent that Are Formally but Not Holomorphically Equivalent to Quadrics
Existence of Real Analytic Surfaces with Hyperbolic Complex Tangent that Are Formally but Not Holomorphically Equivalent to Quadrics
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DOI：
10.1512/iumj.2004.53.2386
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发表时间：
2004
影响因子：
1.1
通讯作者：
Xianghong Gong
中科院分区：
文献类型：
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作者：
Xianghong Gong
我们将证明c2中一个实解析曲面的存在性，它与具有双曲复切线的二次曲面形式等价，但不是全纯等价。利用具有非消失的Bishop不变量的复导数的实解析曲面的Moser-Webster全纯对合得到了这一结果。我们的方法还用于证明在原点附近定义的实平面的实解析可逆映射的存在性，这些映射在形式上等价于线性旋转，但在解析上不等价于线性旋转。
We shall prove the existence of a real analytic sur- face in C 2 that is formally but not holomorphically equivalent to a quadratic surface with a hyperbolic complex tangent. The result is obtained through the pair of holomorphic involutions of Moser-Webster for a real analytic surface with a complex tan- gent of non-vanishing Bishop invariant. Our method is also used to show the existence of real analytic reversible maps of the real plane, defined near the origin, that are formally, but not real an- alytically, equivalent to a linear rotation.