### Abstract

We study the rigidity of holomorphic mappings from a neighborhood of a Levi-nondegenerate CR hypersurface M with signature l into a hyperquadric Q^{N}_{l′} ⊆ ℂℙ^{N+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 language | English (US) |
---|---|

Pages (from-to) | 159-190 |

Number of pages | 32 |

Journal | Communications in Analysis and Geometry |

Volume | 23 |

Issue number | 1 |

State | Published - 2015 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Analysis and Geometry*,

*23*(1), 159-190.

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

Research output: Contribution to journal › Article

*Communications in Analysis and Geometry*, vol. 23, no. 1, pp. 159-190.

}

TY - JOUR

T1 - Partial rigidity of CR embeddings of real hypersurfaces into hyperquadrics with small signature difference

AU - Ebenfelt, Peter

AU - Shroff, Ravi

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84914125060&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84914125060&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84914125060

VL - 23

SP - 159

EP - 190

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

SN - 1019-8385

IS - 1

ER -