A new upper bound for the Dirac operator on hypersurfaces

Nicolas Ginoux (1) , Georges Habib (2) , Simon Raulot (3)

1 NWF I - Mathematik
2 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]
3 LMRS - Laboratoire de Mathématiques Raphaël Salem

We prove a new upper bound for the first eigenvalue of the Dirac operator of a compact hypersurface in any Riemannian spin manifold carrying a non-trivial twistor spinor without zeros on the hypersurface. The upper bound is expressed as the first eigenvalue of a drifting Schrödinger operator on the hypersurface. Moreover, using a recent approach developed by O.~Hijazi and S.~Montiel, we completely characterize the equality case when the ambient manifold is the standard hyperbolic space.

Domaines: Géométrie différentielle [math.DG]; Théorie spectrale [math.SP]

Nicolas Ginoux, Georges Habib, Simon Raulot. A new upper bound for the Dirac operator on hypersurfaces: duplicate entry, see hal-01267731 for the original. 2014. ⟨hal-00941566⟩