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

Andrei Moroianu (1) , Liviu Ornea (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 UNIBUC - Université de Bucarest

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 some inequality involving the scalar curvature. In the limiting case the universal cover of the manifold is isometric to a cylinder RxN where N is a manifold admitting Killing spinors.

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu, Liviu Ornea. Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 338, pp.561-564. ⟨10.1016/j.crma.2004.01.030⟩. ⟨hal-00126029v2⟩