A codimension two CR singular submanifold that is formally equivalent to a symmetric quadric
| dc.creator | Huang, Xiaojun | |
| dc.creator | Yin, Wanke | |
| dc.date | 2008-03-01 | |
| dc.date.accessioned | 2026-07-07T09:24:16Z | |
| dc.date.available | 2026-07-07T09:24:16Z | |
| dc.description | Let $M\subset \mathbb{C}^{n+1}$ ($n\geq 2$) be a real analytic submanifold defined by an equation of the form: $w=|z|^2+O(|z|^3)$, where we use $(z,w)\in \mathbb{C}^{n}\times \mathbb{C}$ for the coordinates of $\mathbb{C}^{n+1}$. We first derive a pseudo-normal form for $M$ near 0. We then use it to prove that $(M,0)$ is holomorphically equivalent to the quadric $(M_\infty: w=|z|^2,0)$ if and only if it can be formally transformed to $(M_\infty,0)$. We also use it to give a necessary and sufficient condition when $(M,0)$ can be formally flattened. The result is due to Moser for the case of $n=1$. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0803.0074 | |
| dc.identifier | http://arxiv.org/abs/0803.0074 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156037 | |
| dc.subject | Complex Variables | |
| dc.subject | 32F25 | |
| dc.title | A codimension two CR singular submanifold that is formally equivalent to a symmetric quadric | |
| dc.type | text |