On the Lichnerowicz conjecture for CR manifolds with mixed signature

Jeffrey S. Case, Sean N. Curry, Vladimir S. Matveev

Research output: Contribution to journalArticlepeer-review

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Abstract

We construct examples of nondegenerate CR manifolds with Levi form of signature (p,q), 2≤p≤q, which are compact, not locally CR flat, and admit essential CR vector fields. We also construct an example of a noncompact nondegenerate CR manifold with signature (1,n−1) that is not locally CR flat and admits an essential CR vector field. These provide counterexamples to the analogue of the Lichnerowicz conjecture for CR manifolds with mixed signature.

Original languageEnglish (US)
Pages (from-to)532-537
Number of pages6
JournalComptes Rendus Mathematique
Volume356
Issue number5
DOIs
StatePublished - May 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics

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