Mathematics – Complex Variables
Scientific paper
2002-11-01
Mathematics
Complex Variables
Scientific paper
We consider the class of Levi nondegenerate hypersurfaces $M$ in $\bC^{n+1}$ that admit a local (CR transversal) embedding, near a point $p\in M$, into a standard nondegenerate hyperquadric in $\Bbb C^{N+1}$ 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 $\bC^{N+1}$ 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.
Ebenfelt Peter
Huang Xing
Zaitsev Dmitri
No associations
LandOfFree
The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-364774