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 language | French |
|---|---|
| Pages (from-to) | 532-537 |
| Number of pages | 6 |
| Journal | Comptes Rendus Mathematique |
| Volume | 356 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 1 2018 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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Sur la conjecture de Lichnerowicz pour les variétés CR de signature mixte. / Case, Jeffrey Steven; Curry, Sean N.; Matveev, Vladimir S.
In: Comptes Rendus Mathematique, Vol. 356, No. 5, 01.05.2018, p. 532-537.Research output: Contribution to journal › Article
TY - JOUR
T1 - Sur la conjecture de Lichnerowicz pour les variétés CR de signature mixte
AU - Case, Jeffrey Steven
AU - Curry, Sean N.
AU - Matveev, Vladimir S.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85045027275&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85045027275&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2018.03.012
DO - 10.1016/j.crma.2018.03.012
M3 - Article
VL - 356
SP - 532
EP - 537
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 5
ER -