The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics
By P. Ebenfelt, Xiaojun Huang, D. Zaitsev. 2002
74 citations recorded by the source corpus.
We consider the class of Levi nondegenerate hypersurfaces M in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] that admit a local (CR transversal) embedding, near a point p e M , into a standard nondegenerate hyperquadric in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] with codimension k := N - n small compared to the CR dimension n of M . We show that, for hypersurfaces in this class, there is a normal form (which is closely related to the embedding) such that any local equivalence between two hypersurfaces in normal form must be an automorphism of the associated tangent hyperquadric. We also show that if the signature of M and that of the standard hyperquadric in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] are the same, then the embedding is rigid in the sense that any other embedding must be the original embedding composed with an automorphism of the quadric.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b3e3778a1c92b164e2d1c4e61089b83571f0abfe
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Holomorphic mappings between hyperquadrics with small signature difference (2009, methodology): “ction in (z,ξ¯). Then A(z,ξ¯) ≡ 0. Lemma 2.1 was proved in [Hu1] (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 t”
- Super-rigidity for holomorphic mappings between hyperquadrics with positive signature (2005, methodology): “6, Part (i), was first obtained in ajoint work of the second author with Ebenfelt and Zaitsev [9].”