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On the CR Transversality of Holomorphic Maps into Hyperquadrics

Dedicated to Professor Yum-Tong Siu on the occasion of his 70th birthday
  • Xiaojun HuangEmail author
  • Yuan Zhang
Conference paper
Part of the Abel Symposia book series (ABEL, volume 10)

Abstract

Let M be a smooth Levi-nondegenerate hypersurface of signature in C n with n ≥ 3, and write H N for the standard hyperquadric of the same signature in C N with \(N - n <\frac{n-1} {2}\). Let F be a holomorphic map sending M into \(H_{\ell}^{N}\). Assume F does not send a neighborhood of M in C n into \(H_{\ell}^{N}\). We show that F is necessarily CR transversal to M at any point. Equivalently, we show that F is a local CR embedding from M into \(H_{\ell}^{N}\).

Keywords

Power Series Expansion Open Dense Subset Quantitative Version Weighted Degree Rigidity Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Part of work was done when the authors were attending the 7th Workshop on geometric analysis of PDE and several complex variables at Serra Negra, Brazil. Both authors would like to thank the organizers for the kind invitation. The second author is also indebted to Wuhan University for the hospitality during her several visits there.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Partially supported in part by National Science Foundation DMS-1363418, Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Partially supported in part by National Science Foundation DMS-1265330, Department of Mathematical SciencesIndiana University – Purdue UniversityFort WayneUSA

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