Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length

Abstract

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 R×N where N is a manifold admitting Killing spinors. To cite this article: A. Moroianu, L. Ornea, C. R. Acad. Sci. Paris, Ser. I 338 (2004).