Sur l'holonomie des variétés pseudo-riemanniennes de signature (2,2 + n)

In this paper, we determinate a class of possible restricted holonomy groups for a non-irreducible indecomposable pseudo-riemannian manifold with signature (2,2 + n). In particular, we deduce that which associated to symmetric spaces; and give some examples of such spaces. Finally, we construct some examples of metrics whose restricted holonomy groups are not closed

Sur l'holonomie des variétés pseudo-riemanniennes de signature (2,2+n)(2,2+n)

In this paper, we determinate a class of possible restricted holonomy groups for a non-irreducible indecomposable pseudo-riemannian manifold with signature $(2,2+n)$. In particular, we deduce that which associated to symmetric spaces; and give some examples of such spaces. Finally, we construct some examples of metrics whose restricted holonomy groups are not closed

Pseudo-Riemannian manifolds with recurrent spinor fields

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their holonomy algebras: Riemannian manifolds; Lorentzian manifolds; pseudo-Riemannian manifolds with irreducible holonomy algebras; pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions.Comment: 13 pages, the final versio

Sur l'holonomie des variétés pseudo-riemanniennes de signature (2,2 + n)

In this paper, we determinate a class of possible restricted holonomy groups for a non-irreducible indecomposable pseudo-riemannian manifold with signature (2,2 + n). In particular, we deduce that which associated to symmetric spaces; and give some examples of such spaces. Finally, we construct some examples of metrics whose restricted holonomy groups are not closed

SEIBERG–WITTEN EQUATIONS ON FOUR-DIMENSIONAL LORENTZIAN Spin c

WOS: 000292778200001New kind of spinors are introduced on four-dimensional Lorentzian Spin(c) manifolds in [1]. We define Dirac operator on such spinors. In [2] Seiberg-Witten-like equations are written down on Minkowski space. In the present work we generalize these equations to four-dimensional Lorentzian Spin(c)-manifolds