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

Wanke Yin, Yuan Yuan, Yuan Zhang

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)526-550
Number of pages25
JournalJournal of Geometric Analysis
Volume30
Issue number1
DOIs
StatePublished - Jan 1 2020

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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