Comptes Rendus
Differential Geometry
Almost harmonic spinors
[Spineurs presque harmoniques]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 811-814.

Nous montrons que, sur toute variété spinorielle compacte sans bord non difféomorphe à la sphère de dimension deux, il existe une suite de métriques riemanniennes de volume un pour laquelle la plus petite valeur propre non nulle de l'opérateur de Dirac tend vers zéro. Comme application, nous comparons le spectre de l'opérateur de Dirac avec le volume conforme.

We show that any closed spin manifold not diffeomorphic to the two-sphere admits a sequence of volume-one-Riemannian metrics for which the smallest non-zero Dirac eigenvalue tends to zero. As an application, we compare the Dirac spectrum with the conformal volume.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.06.010

Nicolas Ginoux 1 ; Jean-François Grosjean 2

1 NWF I – Mathematik, Universität Regensburg, 93040 Regensburg, Germany
2 Institut Élie-Cartan (mathématiques), Université Henri Poincaré Nancy I, B.P. 239 54506 Vandoeuvre-Lès-Nancy cedex, France
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Nicolas Ginoux; Jean-François Grosjean. Almost harmonic spinors. Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 811-814. doi : 10.1016/j.crma.2010.06.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.06.010/

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