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

Research output: Contribution to journalArticle

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 languageFrench
Pages (from-to)532-537
Number of pages6
JournalComptes Rendus Mathematique
Volume356
Issue number5
DOIs
StatePublished - May 1 2018

Fingerprint

CR Manifold
Signature
Vector Field
Levi Form
Locally Compact
Counterexample
Analogue

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Case, Jeffrey Steven ; Curry, Sean N. ; Matveev, Vladimir S. / Sur la conjecture de Lichnerowicz pour les variétés CR de signature mixte. In: Comptes Rendus Mathematique. 2018 ; Vol. 356, No. 5. pp. 532-537.
@article{0cf6dea499f84eaa8d0e3275a65cdf4c,
title = "Sur la conjecture de Lichnerowicz pour les vari{\'e}t{\'e}s CR de signature mixte",
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.",
author = "Case, {Jeffrey Steven} and Curry, {Sean N.} and Matveev, {Vladimir S.}",
year = "2018",
month = "5",
day = "1",
doi = "10.1016/j.crma.2018.03.012",
language = "French",
volume = "356",
pages = "532--537",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier Masson",
number = "5",

}

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 journalArticle

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 -