“Geometry” of spin 3 gauge theories
Grafting Seiberg-Witten monopoles.
Introduction élémentaire à l'analyse spinorielle
Invariant torsion and G2-metrics
We introduce and study a notion of invariant intrinsic torsion geometrywhich appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S3. This space is foliated by sixdimensional hypersurfaces, each of which carries a particular type of SO(3)-structure; the intrinsic torsion is invariant under SO(3). The last condition is sufficient to imply local homogeneity of such geometries, and this allows us to give a classification. We close the circle by showing that...
-Dirac operator and the Cartan-Kähler theorem
We apply the Cartan-Kähler theorem for the k-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for the tableaux of the first prolongations of these two operators are involutive. This gives us a new characterization of the set of initial conditions for the 2-Dirac operator.
Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz
We describe all compact spin Kähler manifolds of even complex dimension and positive scalar curvature with least possible first eigenvalue of the Dirac operator.
Killing spinor-valued forms and the cone construction
On a pseudo-Riemannian manifold we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on and parallel fields on the metric cone over for spinor-valued forms.
La première valeur propre d’opérateurs de Dirac sur les variétés à bord et quelques applications
Dans cet article, on s’intéresse à l’aspect conforme du spectre d’opérateurs de Dirac dans le cadre des variétés à bord. Dans un premier temps, on étudie la première valeur propre de l’opérateur de Dirac sous la condition associée à un opérateur de chiralité conduisant à la définition d’un nouvel invariant spinoriel conforme. Dans la dernière partie, on s’intéresse à l’opérateur de Dirac du bord en reliant sa première valeur propre à des invariants reflétant la géométrie extrinsèque du bord. Dans...
Mass endomorphism, surgery and perturbations
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.
Moments and Huygens' principle for conformally invariant field equations in curved space-times
Monogenic functions in conformal geometry.
Monogenic functions on surfaces.
Monopoles over 4-manifolds containing long necks. I.
Nonlinear connections and spinor geometry.
On conformal powers of the Dirac operator on spin manifolds
The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the Dirac operator....
On the eta invariant, stable positive scalar curvature, and Higher -genera.
On the existence of a geometrical interpretation of spinors of the various pseudo-euclidean spaces of dimension 3 and 4 by means of real, irreducible tensors of rank p
On the geometry of Riemannian manifolds with a Lie structure at infinity.
On the spinorial representations of .
Positive scalar curvature and the Dirac operator on complete riemannian manifolds