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 both Sasakian and 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.
@article{bwmeta1.element.doi-10_2478_s11533-010-0060-1,
author = {Nicolas Ginoux and Georges Habib},
title = {A spectral estimate for the Dirac operator on Riemannian flows},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {950-965},
zbl = {1221.53054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0060-1}
}
Nicolas Ginoux; Georges Habib. A spectral estimate for the Dirac operator on Riemannian flows. Open Mathematics, Tome 8 (2010) pp. 950-965. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0060-1/
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