Normal forms of real surfaces under unimodular transformations near elliptic complex tangents
Normal forms of real surfaces under unimodular transformations near elliptic complex tangents
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DOI：
10.1215/s0012-7094-94-07407-3
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发表时间：
1994-04
影响因子：
2.5
通讯作者：
Xianghong Gong
中科院分区：
文献类型：
--
作者：
Xianghong Gong
其中q（zi,）是z和l的收敛幂级数从三阶项开始。7 in（1.1）是一个单模不变量，I1是Bishop不变量[1]。根据0 < I1 < 1/2、I11/2或1/2 < I1，复切线被称为椭圆型、抛物线型或双曲型。J. K. Moser和S. M. Webster在1999年系统地研究了坐标生物全纯变换下（1.1）式的实解析曲面的范式。在[2]中进一步研究了全纯单模变换下实解析曲面的范式问题，其中Moser-Webster范式起了重要作用。特别地，证明了在全纯非模变换下，具有非消失Bishop不变量的椭圆复切线附近的实解析曲面可以转化为正规形式。本文讨论了椭圆复切线与y = 0附近曲面的正规形式。
in which q(zi, ) is a convergent power series in z and l starting with the terms of the third order. The 7 in (1.1) is a unimodular invariant and I1 is the Bishop invariant [1]. The complex tangent is said to be elliptic, parabolic, or hyperbolic according to 0 < I1 < 1/2, I11/2 or 1/2 < I1 < . In [4], J. K. Moser and S. M. Webster investigated systematically the normal forms of real analytic surfaces in the form (1.1) under the biholomorphic change of coordinates. The problem of normal forms of real analytic surfaces under holomorphic unimodular transformations was further studied in [2], where the Moser-Webster normal form played an important role. In particular, it was shown that a real analytic surface near an elliptic complex tangent with nonvanishing Bishop invariant can be transformed into a normal form under holomorphic unimodular transformations. In this paper, we discuss the normal form of surfaces near an elliptic complex tangent with y 0.