On the Lichnerowicz conjecture for CR manifolds with mixed signature

  title={On the Lichnerowicz conjecture for CR manifolds with mixed signature},
  author={Jeffrey S. Case and Sean N. Curry and Vladimir S. Matveev},
  journal={Comptes Rendus Mathematique},
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. 


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