Spherical space forms, CR mappings, and proper maps between balls

John P. D'Angelo, Daniel A. Lichtblau

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)391-415
Number of pages25
JournalThe Journal of Geometric Analysis
Volume2
Issue number5
DOIs
StatePublished - 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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