On Highly Degenerate CR Maps of Spheres
- Author(s)
- Giuseppe della Sala, Bernhard Lamel, Michael Reiter, Duong Ngoc Son
- 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.
- Organisation(s)
- Department of Mathematics
- External organisation(s)
- American University of Beirut, Faculty of Fundamental Sciences, Phenikaa University
- Journal
- Journal of Geometric Analysis
- Volume
- 34
- ISSN
- 1050-6926
- DOI
- https://doi.org/10.1007/s12220-023-01495-4
- Publication date
- 03-2024
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis, 101009 Geometry
- Keywords
- ASJC Scopus subject areas
- Geometry and Topology
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/c75c8d47-f55d-4fe5-b1c8-d77b9b43e93d