Rigidity of CR-immersions into spheres
By P. Ebenfelt, Xiaojun Huang, D. Zaitsev. 2002
75 citations recorded by the source corpus.
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 $\phi\circ f$, 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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1485275520680098328c6e7ddecfcd76907863ea
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Holomorphic mappings between hyperquadrics with small signature difference (2009, methodology): “ (see Lemma 3.2, [Hu1]). In that paper, the lemma is stated only for ℓ= 0, but the proof for ℓ>0 is identical (see also Lemma 2.1 in [EHZ2]). Lemma 2.1 was also a crucial tool in the papers [Hu1], [EHZ1], [EHZ2]. We shall also need the following corollary, which follows from repeated use of Lemma”
- The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics (2002, methodology): “The case of smooth CR embeddings in Theorem 1.6, for � = 0 and k1 = k2, was also treated, by a different method, in the authors’ recent paper [ EHZ02 ] and previously, for k1 = k2 = 1, by Webster [W79].”