The Hijazi inequalities on complete Riemannian manifolds.
Nakad, Roger (2011)
Advances in Mathematical Physics
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Displaying similar documents to “A spectral estimate for the Dirac operator on Riemannian flows”
The Hijazi inequalities on complete Riemannian manifolds.
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. ...
Curvature properties of φ-null Osserman Lorentzian S-manifolds
Letizia Brunetti, Angelo Caldarella (2014)
Open Mathematics
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We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian S-manifold and the Jacobi operators with respect to particular spacelike unit vectors. We study the number of the eigenvalues of such operators on Lorentzian S-manifolds satisfying the φ-null Osserman condition, under suitable assumptions on the dimension of the manifold. Then, we provide in full generality a new curvature characterization for Lorentzian S-manifolds...
A new example of compact Riemannian manifold with structure group Spin(7)
Fernández, Marisa (1987)
Portugaliae mathematica
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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...
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.