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

  • Wanke YinEmail author
  • Yuan Yuan
  • Yuan Zhang


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.


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

Mathematics Subject Classification




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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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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