Prescribing mean curvature: existence and uniqueness problems.
Prolongement des structures spinorielles
Rarita-Schwinger type operators on spheres and real projective space
In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger...
Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces
Any Kähler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dimension.
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 .
The cohomology groups
The eta invariant and metrics of positive scalar curvature.
The even Clifford structure of the fourth Severi variety
TheHermitian symmetric spaceM = EIII appears in the classification of complete simply connected Riemannian manifolds carrying a parallel even Clifford structure [19]. This means the existence of a real oriented Euclidean vector bundle E over it together with an algebra bundle morphism φ : Cl0(E) → End(TM) mapping Ʌ2E into skew-symmetric endomorphisms, and the existence of a metric connection on E compatible with φ. We give an explicit description of such a vector bundle E as a sub-bundle of End(TM)....
The generalized Lichnerowicz formula and analysis of Dirac operators.
The Hijazi inequalities on complete Riemannian manifolds.
The laplacian and the Dirac operator in infinitely many variables
The Srní lectures on non-integrable geometries with torsion
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...