Comptes Rendus
no. 2
Differential geometry
Rigidity in a conformal class of contact form on CR manifold
[Rigidité dans une classe conforme de formes de contact sur une variété CR]

Présenté par : Haïm Brézis

Pak Tung Ho1
1 Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 167-172.

Dans cet article, nous montrons d'abord que deux formes de contact conformes quelconques sur une variété compacte CR qui ont la même courbure de Ricci pseudo-hermitienne ne diffèrent que d'un facteur constant. Dans une autre direction, nous prouvons un analogue CR du lemme de Schwarz conforme de la géométrie riemannienne.

In this paper, we first prove that any two conformal contact forms on a compact CR manifold that have the same pseudo-Hermitian Ricci curvature must be different by a constant. In another direction, we prove a CR analogue of the conformal Schwarz lemma of Riemannian geometry.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.11.010
Pak Tung Ho 1

1 Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea 
@article{CRMATH_2015__353_2_167_0,
     author = {Pak Tung Ho},
     title = {Rigidity in a conformal class of contact form on {CR} manifold},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {167--172},
     publisher = {Elsevier},
     volume = {353},
     number = {2},
     year = {2015},
     doi = {10.1016/j.crma.2014.11.010},
     language = {en},
}
TY  - JOUR
AU  - Pak Tung Ho
TI  - Rigidity in a conformal class of contact form on CR manifold
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 167
EP  - 172
VL  - 353
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crma.2014.11.010
LA  - en
ID  - CRMATH_2015__353_2_167_0
ER  - 
%0 Journal Article
%A Pak Tung Ho
%T Rigidity in a conformal class of contact form on CR manifold
%J Comptes Rendus. Mathématique
%D 2015
%P 167-172
%V 353
%N 2
%I Elsevier
%R 10.1016/j.crma.2014.11.010
%G en
%F CRMATH_2015__353_2_167_0
Pak Tung Ho. Rigidity in a conformal class of contact form on CR manifold. Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 167-172. doi : 10.1016/j.crma.2014.11.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.11.010/

[1] S. Dragomir; G. Tomassini Differential Geometry and Analysis on CR Manifolds, Progress in Mathematics, vol. 246, Birkhäuser Boston, Boston, MA, USA, 2006

[2] P.T. Ho The long time existence and convergence of the CR Yamabe flow, Commun. Contemp. Math., Volume 14 (2012) no. 2 article ID (50 p.)

[3] P.T. Ho Results related to prescribing pseudo-Hermitian scalar curvature, Int. J. Math., Volume 24 (2013) no. 3 article ID 1350020 (29 p.)

[4] D. Jerison; J.M. Lee The Yamabe problem on CR manifolds, J. Differ. Geom., Volume 25 (1987), pp. 167-197

[5] O. Kobayaski Scalar curvature of a metric with unit volume, Math. Ann., Volume 279 (1987), pp. 253-265

[6] J.M. Lee The Fefferman metric and pseudohermitian invariants, Trans. Amer. Math. Soc., Volume 296 (1986), pp. 411-429

[7] P. Suárez-Serrato; S. Tapie Conformal entropy rigidity through Yamabe flows, Math. Ann., Volume 353 (2012), pp. 333-357

[8] X. Xu Prescribing a Ricci tensor in a conformal class of Riemannian metrics, Proc. Amer. Math. Soc., Volume 115 (1992), pp. 455-459

[9] S.T. Yau Remarks on conformal transformations, J. Differ. Geom., Volume 8 (1973), pp. 369-381

[10] Y. Zhang The contact Yamabe flow, University of Hanover, Germany, 2006 (Ph.D. thesis)

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

The Webster scalar curvature problem on higher dimensional CR compact manifolds

Hichem Chtioui

C. R. Math (2007)

Prescribing the Webster scalar curvature on CR spheres

Ridha Yacoub

C. R. Math (2011)

CR-invariants and the scattering operator for complex manifolds with CR-boundary

Peter D. Hislop; Peter A. Perry; Siu-Hung Tang

C. R. Math (2006)