The Dirac operator on collapsing -bundles
Bernd Ammann (1997-1998)
Séminaire de théorie spectrale et géométrie
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Displaying similar documents to “The Hijazi inequalities on complete Riemannian manifolds.”
The Dirac operator on collapsing -bundles
A spectral estimate for the Dirac operator on Riemannian flows
Nicolas Ginoux, Georges Habib (2010)
Open Mathematics
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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.
On the conformal relation between twistors and Killing spinors
Friedrich, Thomas
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[For the entire collection see Zbl 0699.00032.] The author considers the conformal relation between twistors and spinors on a Riemannian spin manifold of dimension . A first integral is constructed for a twistor spinor and various geometric properties of the spin manifold are deduced. The notions of a conformal deformation and a Killing spinor are considered and such a deformation of a twistor spinor into a Killing spinor and conditions for the equivalence of these quantities is indicated. ...
Skew Killing spinors
Georges Habib, Julien Roth (2012)
Open Mathematics
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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.
Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz
Andrei Moroianu (1999)
Annales de l'institut Fourier
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We describe all compact spin Kähler manifolds of even complex dimension and positive scalar curvature with least possible first eigenvalue of the Dirac operator.
Lorentzian manifolds with special holonomy and parallel spinors
Leistner, Thomas
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The author studies the holonomy group of a simply connected indecomposable and reducible Lorentzian spin manifold under the condition that they admit parallel spinors. He shows that there are only two possible situations: either the manifold is a so-called Brinkmann wave or it has Abelian holonomy and is a pp-manifold – a generalization of a plane-wave. The author gives also sufficient conditions for a Brinkmann wave to have as holonomy the semidirect product of holonomy group of a Riemannian...