Schémas d'Einstein-Dirac en spin 1/2 et généralisations
Skew Killing spinors
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.
Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds.
Spectrum of twisted Dirac operators on the complex projective space
In this paper, we explicitly determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles over the complex projective space for .
Spinors on in supergravity
Structures de Weyl admettant des spineurs parallèles
Surfaces in and via spinors
We generalize the spinorial characterization of isometric immersions of surfaces in given by T. Friedrich to surfaces in and . The main argument is the interpretation of the energy-momentum tensor associated with a special spinor field as a second fundamental form. It turns out that such a characterization of isometric immersions in terms of a special section of the spinor bundle also holds in the case of hypersurfaces in the Euclidean -space.
Symplectic spinor valued forms and invariant operators acting between them
Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.
Symplectic twistor operator and its solution space on
We introduce the symplectic twistor operator in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension 1. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on .