TY - JOUR
T1 - Sur la conjecture de Lichnerowicz pour les variétés CR de signature mixte
AU - Case, Jeffrey S.
AU - Curry, Sean N.
AU - Matveev, Vladimir S.
N1 - Funding Information:
JSC was supported by a grant from the Simons Foundation (Grant No. 524601).
Funding Information:
JSC was supported by a grant from the Simons Foundation (Grant No. 524601 ).
Publisher Copyright:
© 2018 Académie des sciences
PY - 2018/5
Y1 - 2018/5
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.
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U2 - 10.1016/j.crma.2018.03.012
DO - 10.1016/j.crma.2018.03.012
M3 - Article
AN - SCOPUS:85045027275
VL - 356
SP - 532
EP - 537
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 5
ER -