A spectral estimate for the Dirac operator on Riemannian flows

Nicolas Ginoux (1) , Georges Habib (2)

1 NWF I - Mathematik
2 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]

We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on Sasakian and on $3$-dimensional manifolds and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.

Mots clés: Estimation of eigenvalues; upper and lower bounds; Foliations; Sasakian manifolds; Spin Geometry; Spectral geometry

Domaines: Géométrie différentielle [math.DG]

Nicolas Ginoux, Georges Habib. A spectral estimate for the Dirac operator on Riemannian flows. Central European Journal of Mathematics, 2010, 8, pp.950-965. ⟨hal-00523746⟩