Partial rigidity of CR embeddings of real hypersurfaces into hyperquadrics with small signature difference

Peter Ebenfelt, Ravi Shroff

Research output: Contribution to journalArticle

Abstract

We study the rigidity of holomorphic mappings from a neighborhood of a Levi-nondegenerate CR hypersurface M with signature l into a hyperquadric QNl′ ⊆ 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 a dimension depending only on the CR complexity and the signature difference, but not on 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.

Original languageEnglish (US)
Pages (from-to)159-190
Number of pages32
JournalCommunications in Analysis and Geometry
Volume23
Issue number1
StatePublished - 2015

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Real Hypersurfaces
Rigidity
Signature
Partial
Holomorphic Mappings
Quadric
Degeneracy
Argand diagram
Hypersurface
Theorem

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

Cite this

Partial rigidity of CR embeddings of real hypersurfaces into hyperquadrics with small signature difference. / Ebenfelt, Peter; Shroff, Ravi.

In: Communications in Analysis and Geometry, Vol. 23, No. 1, 2015, p. 159-190.

Research output: Contribution to journalArticle

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