Rigidity of CRimmersions into spheres
Abstract
We consider local CRimmersions 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 $\phi\circ f$, where $\phi$ 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2002
 DOI:
 10.48550/arXiv.math/0206152
 arXiv:
 arXiv:math/0206152
 Bibcode:
 2002math......6152E
 Keywords:

 Complex Variables;
 Differential Geometry