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 language | English |
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Article number | 80 |
Journal | Journal of Geometric Analysis |
Volume | 34 |
Issue number | 3 |
DOIs | |
Publication status | Published - Mar 2024 |
Austrian Fields of Science 2012
- 101002 Analysis
- 101009 Geometry
Keywords
- CR map
- Sphere