论文标题
正常形式，移动框架和差异不变的c^2
Normal forms, moving frames, and differential invariants for nondegenerate hypersurfaces in C^2
论文作者
论文摘要
我们使用均等移动帧的方法来重新审视正常形式的问题，并在全体形态转换的伪组作用下，无效的真实超曲面M \子集C^2。移动的框架复发公式使我们能够系统地和算法恢复Chern和Moser的结果，用于在M的一个开放社区中在M点P \或Umbilic处于非bumillic的超曲面的结果。在前一种情况下，正常形式扩展的系数在该点的高度表面射流时表示，提供了一个完整的功能独立差异不变的系统，可用于解决等效问题。 We prove that under a suitable genericity condition, the entire algebra of differential invariants for such hypersurfaces can be generated, through the operators of invariant differentiation, by a single real differential invariant of order 7. We then apply moving frames to construct new convergent normal forms for nondegenerate real hypersurfaces at singularly umbilic points, namely those umbilic points where the hypersurface is not identically他们周围的脐带。
We use the method of equivariant moving frames to revisit the problem of normal forms and equivalence of nondegenerate real hypersurfaces M \subset C^2 under the pseudo-group action of holomorphic transformations. The moving frame recurrence formulae allow us to systematically and algorithmically recover the results of Chern and Moser for hypersurfaces that are either non-umbilic at a point p \in M or umbilic in an open neighborhood of it. In the former case, the coefficients of the normal form expansion, when expressed as functions of the jet of the hypersurface at the point, provide a complete system of functionally independent differential invariants that can be used to solve the equivalence problem. We prove that under a suitable genericity condition, the entire algebra of differential invariants for such hypersurfaces can be generated, through the operators of invariant differentiation, by a single real differential invariant of order 7. We then apply moving frames to construct new convergent normal forms for nondegenerate real hypersurfaces at singularly umbilic points, namely those umbilic points where the hypersurface is not identically umbilic around them.
