On Highly Degenerate CR Maps of Spheres

Giuseppe della Sala, Bernhard Lamel, Michael Reiter, Duong Ngoc Son

Publications: Contribution to journalArticlePeer Reviewed

Abstract

For N≥ 4 we classify the (N- 3) -degenerate smooth CR maps of the three-dimensional unit sphere into the (2 N- 1) -dimensional unit sphere. Each of these maps has image being contained in a five-dimensional complex-linear space and is of degree at most two, or equivalent to one of the four maps into the five-dimensional sphere classified by Faran. As a byproduct of our classification we obtain new examples of rational maps of degree three which are (N- 3) -degenerate only along a proper real subvariety and are not equivalent to polynomial maps. In particular, by changing the base point, it is possible to construct new families of nondegenerate maps.

Original languageEnglish
Article number80
JournalJournal of Geometric Analysis
Volume34
Issue number3
DOIs
Publication statusPublished - Mar 2024

Austrian Fields of Science 2012

  • 101002 Analysis
  • 101009 Geometry

Keywords

  • CR map
  • Sphere

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