Rigidity of CR-immersions into spheres
| dc.creator | Ebenfelt, Peter | |
| dc.creator | Huang, Xiaojun | |
| dc.creator | Zaitsev, Dmitri | |
| dc.date | 2002-06-15 | |
| dc.date.accessioned | 2026-07-07T04:49:08Z | |
| dc.date.available | 2026-07-07T04:49:08Z | |
| dc.description | We consider local CR-immersions of a strictly pseudoconvex real hypersurface $M\subset\bC^{n+1}$, near a point $p\in M$, into the unit sphere $\mathbb S\subset\bC^{n+d+1}$ with $d>0$. Our main result is that if there is such an immersion $f\colon (M,p)\to \mathbb S$ and $d < n/2$, then $f$ is {\em rigid} in the sense that any other immersion of $(M,p)$ into $\mathbb S$ is of the form $ϕ\circ f$, where $ϕ$ is a biholomorphic automorphism of the unit ball $\mathbb B\subset\bC^{n+d+1}$. As an application of this result, we show that an isolated singularity of an irreducible analytic variety of codimension $d$ in $\bC^{n+d+1}$ is uniquely determined up to affine linear transformations by the local CR geometry at a point of its Milnor link. | |
| dc.identifier | https://arxiv.org/abs/math/0206152 | |
| dc.identifier | http://arxiv.org/abs/math/0206152 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64310 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.title | Rigidity of CR-immersions into spheres | |
| dc.type | text |