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The CR Immersion into a Sphere with the Degenerate CR Gauss Map

  • Wanke YinEmail author
  • Yuan Yuan
  • Yuan Zhang
Article
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Abstract

It is a classical problem in algebraic geometry to characterize the algebraic subvariety by using the Gauss map. In this note, we study the analogous phenomenon in CR geometry. In particular, under some assumptions, we show that a CR map between spheres is totally geodesic if and only if the CR Gauss map of the image is degenerate.

Keywords

Proper holomorphic map Degenerate Gauss map Normal form Geometric rank Degeneracy rank 

Mathematics Subject Classification

32V30 
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Notes

Acknowledgements

The authors would like to thank Xiaojun Huang and Shanyu Ji for helpful discussions. The authors are also indebted to the referee for many very useful and constructive suggestions and comments.

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© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina
  2. 2.Department of MathematicsSyracuse UniversitySyracuseUSA
  3. 3.Department of MathematicsPurdue UniversityFort WayneUSA

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