论文标题
在更高的codimension中构建$ 2- $喷气式定理的$ 2- $喷气机
Construction of counterexamples to the $2-$jet determination Chern-Moser Theorem in higher codimension
论文作者
论文摘要
我们首先构建了一个通用的二次二次子序列，$ 5 $ 5 $ in $ \ bbb c^9 $，它承认了一个真正的分析性无限cr自动形态，并具有同质的多项式系数$4。$4。 然后，我们提供了足够的条件，以在更高的consimension中为$ 2- $ JET确定Chern-Moser定理生成更多的反例。特别是，我们构建了通用二次次级manifolds的示例，并确定了任意高阶的JET。
We first construct a counterexample of a generic quadratic submanifold of codimension $5$ in $\Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $4.$ This example also resolves a question in the Tanaka prolongation theory that was open for more than 50 years. Then we give sufficient conditions to generate more counterexamples to the $2-$jet determination Chern-Moser Theorem in higher codimension. In particular, we construct examples of generic quadratic submanifolds with jet determination of arbitrarily high order.
