Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces

Hassan Boualem; Marc Herzlich

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 2, page 461-469
  • ISSN: 0391-173X

Abstract

top
Any Kähler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dimension.

How to cite

top

Boualem, Hassan, and Herzlich, Marc. "Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.2 (2002): 461-469. <http://eudml.org/doc/84477>.

@article{Boualem2002,
abstract = {Any Kähler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dimension.},
author = {Boualem, Hassan, Herzlich, Marc},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {2},
pages = {461-469},
publisher = {Scuola normale superiore},
title = {Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces},
url = {http://eudml.org/doc/84477},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Boualem, Hassan
AU - Herzlich, Marc
TI - Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 2
SP - 461
EP - 469
AB - Any Kähler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dimension.
LA - eng
UR - http://eudml.org/doc/84477
ER -

References

top
  1. [1] L. Andersson – M. Dahl, Scalar curvature rigidity for asymptotically locally hyperbolic manifolds, Ann. Global Anal. Geom. 16 (1998), 1-27. Zbl0946.53021MR1616570
  2. [2] C. Bär, Real Killing spinors and holonomy, Comm. Math. Phys. 154 (1993), 509-521. Zbl0778.53037MR1224089
  3. [3] A. L. Besse, “Einstein manifolds”, Ergeb. Math. Grenzgeb., Band 10, Springer, Berlin, 1981. Zbl0613.53001MR2371700
  4. [4] O. Biquard, “Métriques d’Einstein asymptotiquement symétriques”, Astérisque, vol. 265, Soc. math. France, 2000. Zbl0967.53030
  5. [5] C. R. Graham – J. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 (1991), 186-225. Zbl0765.53034MR1112625
  6. [6] M. Herzlich, Scalar curvature and rigidity for odd-dimensional complex hyperbolic spaces, Math. Ann. 312 (1998), 641-657. Zbl0946.53022MR1660251
  7. [7] K. D. Kirchberg, Killing spinors on Kähler manifolds, Ann. Global Anal. Geom. 11 (1993), 141-164. Zbl0810.53033MR1225435
  8. [8] M. C. Leung, Pinching theorem on asymptotically hyperbolic spaces, Internat. J. Math. 4 (1993), 841-857. Zbl0810.53032MR1245353
  9. [9] M. Min-Oo, Scalar curvature rigidity of asymptotically hyperbolic spin manifolds, Math. Ann. 285 (1989), 527-539. Zbl0686.53038MR1027758
  10. [10] A. Moroianu, La première valeur propre de l’opérateur de Dirac sur les variétés kähleriennes compactes, Comm. Math. Phys. 169 (1995), 373-384. Zbl0832.53054MR1329200
  11. [11] A. Moroianu, S pin c manifolds and complex contact structures, Comm. Math. Phys. 193 (1998), 661-674. Zbl0908.53024MR1624855

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.