On Kirchberg's Inequality for Compact Kähler Manifolds of Even Complex Dimension

Abstract : In 1986 Kirchberg showed that each eigenvalue of the Dirac operator on a compact Kähler manifold of even complex dimension satisfies some inequality involving the scalar curvature. It is conjectured that the manifolds for the limiting case of this inequality are products T^2×N, where T^2 is a flat torus and N is the twistor space of a quaternionic Kähler manifold of positive scalar curvature. In 1990 Lichnerowicz announced an affirmative answer for this conjecture, but his proof seems to work only when assuming that the Ricci tensor is parallel. The aim of this note is to prove several results about manifolds satisfying the limiting case of Kirchberg''s inequality and to prove the above conjecture in some particular cases.
Type de document :
Article dans une revue
Annals of Global Analysis and Geometry, Springer Verlag, 1997, 15, pp.235-242. 〈10.1023/A:1006543304443〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00125983
Contributeur : Andrei Moroianu <>
Soumis le : mardi 23 janvier 2007 - 11:28:57
Dernière modification le : jeudi 9 février 2017 - 15:16:47
Document(s) archivé(s) le : mercredi 7 avril 2010 - 02:27:42

Fichiers

1997agag.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Andrei Moroianu. On Kirchberg's Inequality for Compact Kähler Manifolds of Even Complex Dimension. Annals of Global Analysis and Geometry, Springer Verlag, 1997, 15, pp.235-242. 〈10.1023/A:1006543304443〉. 〈hal-00125983〉

Partager

Métriques

Consultations de la notice

161

Téléchargements de fichiers

111