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

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 $\text{λ}{}^2\text{?}\text{n?1}\text{4(n?2)}\text{inf}{}_{\mathrm{M}}\text{Scal}$. In the limiting case the universal cover of the manifold is isometric to $\text{R}\text{×N}$ 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).