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 λ 2 ≥ n−1 4(n−2) infM Scal. In the limiting case the universal cover of the manifold is isometric to R×N where N is a manifold admitting Killing spinors. Estimations de valeurs… CONTINUE READING