Comptes Rendus
no. 7
Differential Geometry
Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length
[Estimations de valeurs propres pour l'opérateur de Dirac et 1-formes harmoniques de longueur constante]

Présenté par : Marcel Berger

Andrei Moroianu1 ; Liviu Ornea2
1 Centre de mathémathiques, École polytechnique, 91128 Palaiseau cedex, France
2 University of Bucharest, Faculty of Mathematics, 14 Academiei str., 70109 Bucharest, Romania
Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 561-564.

Nous démontrons que toute valeur propre λ de l'opérateur de Dirac d'une variété spinorielle compacte, de dimension n, qui admet une 1-forme harmonique non-triviale de longueur constante vérifie l'inégalité λ2⩾n-14(n-2)infMScal. Dans le cas limite le revêtement universel de la variété est isométrique à ℝ×N où N est une variété admettant des spineurs de Killing.

We prove that on a compact n-dimensional spin manifold admitting a non-trivial harmonic 1-form of constant length, every eigenvalue λ of the Dirac operator satisfies the inequality λ2⩾n-14(n-2)infMScal. In the limiting case the universal cover of the manifold is isometric to ℝ×N where N is a manifold admitting Killing spinors.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.01.030

Andrei Moroianu 1 ; Liviu Ornea 2

1 Centre de mathémathiques, École polytechnique, 91128 Palaiseau cedex, France
2 University of Bucharest, Faculty of Mathematics, 14 Academiei str., 70109 Bucharest, Romania 
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Andrei Moroianu; Liviu Ornea. Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length. Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 561-564. doi : 10.1016/j.crma.2004.01.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.01.030/

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