Partial Rigidity of CR Embeddings of Real Hypersurfaces into Hyperquadrics with Small Signature Difference
Ebenfelt, Peter · Shroff, Ravi
Original · EN
We study the rigidity of holomorphic mappings from a neighborhood of a Levi-nondegenerate CR hypersurface M with signature l into a hyperquadric Qₗ'ⁿ CPⁿ⁺¹ of larger dimension and signature. We show that if the CR complexity of M is not too large then the image of M under any such mapping is contained in a complex plane with dimension independent of N. This result follows from two theorems, the first demonstrating that for sufficiently degenerate mappings, the image of M is contained in a plane, and the second relating the degeneracy of mappings into different quadrics.
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