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arXiv · 1802.00083

On the Lichnerowicz conjecture for CR manifolds with mixed signature

Jeffrey S. Case·Sean N. Curry·Vladimir S. Matveev
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Abstract

We construct examples of nondegenerate CR manifolds with Levi form of signature $(p,q)$, $2\leq p\leq q$, 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 $(1,n-1)$ which is not locally CR flat and admits an essential CR vector fields. These provide counterexamples to the analogue of the Lichnerowicz conjecture for CR manifolds with mixed signature.

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Jeffrey S. Case, Sean N. Curry, Vladimir S. Matveev. 2018-01-31. On the Lichnerowicz conjecture for CR manifolds with mixed signature. https://doi.org/10.1016/j.crma.2018.03.012

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