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Currently displaying 1 – 3 of 3

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Skew Killing spinors

Georges Habib; Julien Roth — 2012

Open Mathematics

We study the existence of a skew Killing spinor on 2- and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.

A spectral estimate for the Dirac operator on Riemannian flows

Nicolas Ginoux; Georges 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.

Riemannian foliations with parallel or harmonic basic forms

Fida El Chami; Georges Habib; Roger Nakad — 2015

Archivum Mathematicum

In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.

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