A spectral estimate for the Dirac operator on Riemannian flows

by Nicolas Ginoux and Georges Habib

Cent. Eur. J. Math. 8 (2010), no. 5, 950--965

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Abstract: We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We also 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.

Nicolas Ginoux, 10.03.2011