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A spectral estimate for the Dirac operator on Riemannian flows

Nicolas GinouxGeorges Habib — 2010

Open Mathematics

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.

A Singularity Theorem for Twistor Spinors

Florin Alexandru BelgunNicolas GinouxHans-Bert Rademacher — 2007

Annales de l’institut Fourier

We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.

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