Differential Geometry
Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length
Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 561-564.

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 λ 2 n-1 4(n-2) inf M Scal . In the limiting case the universal cover of the manifold is isometric to ×N where N is a manifold admitting Killing spinors.

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 λ 2 n-1 4(n-2) inf M Scal . Dans le cas limite le revêtement universel de la variété est isométrique à ×NN est une variété admettant des spineurs de Killing.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.01.030
Moroianu, Andrei 1; Ornea, Liviu 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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Moroianu, Andrei; Ornea, Liviu. 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. http://www.numdam.org/articles/10.1016/j.crma.2004.01.030/

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