Abstract
We determine precisely for which spherical space forms there are nontrivial smooth CR mappings to spheres. Equivalently we determine for which fixed point free finite unitary groups ⌈ there exists a ⌈-invariant proper holomorphic rational map between balls. The answer is that the group must be cyclic and essentially only two classes of representations can occur. For these there are invariant polynomial examples.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 391-415 |
| Number of pages | 25 |
| Journal | The Journal of Geometric Analysis |
| Volume | 2 |
| Issue number | 5 |
| DOIs | |
| State | Published - Sep 1 1992 |
Keywords
- CR mappings
- Math Subject Classification: 32H35, 57S25, 51F25
- finite unitary groups
- proper holomorphic mappings
- spherical space forms
- unit ball
ASJC Scopus subject areas
- Geometry and Topology
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D'Angelo, J. P., & Lichtblau, D. A. (1992). Spherical space forms, CR mappings, and proper maps between balls. The Journal of Geometric Analysis, 2(5), 391-415. https://doi.org/10.1007/BF02921298