Sur la conjecture de Lichnerowicz pour les variétés CR de signature mixte

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

doi:10.1016/j.crma.2018.03.012

Sur la conjecture de Lichnerowicz pour les variétés CR de signature mixte

Translated title of the contribution: On the Lichnerowicz conjecture for CR manifolds with mixed signature

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

Mathematics

Research output: Contribution to journal › Article

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.

Translated title of the contribution	On the Lichnerowicz conjecture for CR manifolds with mixed signature
Original language	French
Pages (from-to)	532-537
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	356
Issue number	5
DOIs	https://doi.org/10.1016/j.crma.2018.03.012
State	Published - May 2018

All Science Journal Classification (ASJC) codes

Mathematics(all)

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Case, J. S., Curry, S. N., & Matveev, V. S. (2018). Sur la conjecture de Lichnerowicz pour les variétés CR de signature mixte. Comptes Rendus Mathematique, 356(5), 532-537. https://doi.org/10.1016/j.crma.2018.03.012

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