Conformal holonomy, symmetric spaces, and skew symmetric torsion

Conformal holonomy, symmetric spaces, and skew symmetric torsion

We consider the question: can the isotropy representation of an irreducible pseudoRiemannian symmetric space be realized as a conformal holonomy group? Using recent results of Čap, Gover and Hammerl, we study the representations of SO(2, 1), PSU(2, 1) and PSp(2, 1) as isotropy groups of irreducible symmetric spaces of signature (3, 2), (4, 4) and (6, 8), respectively, describing the geometry in...

On the Holonomy of Connections with Skew-symmetric Torsion

We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any non-degenerated 2-form or any spinor. Suitable integral formulas allow us to prove similar properties in case of a compact Riemannian manifold equipped with a metric connection of skew-sy...

Conformal Vector Fields in Symmetric and Conformal Symmetric Spaces

Consequences of the existence of conformal vector fields in (locally) symmetric and conformal symmetric spaces, have been obtained. An attempt has been made for a physical interpretation of the consequences in the framework of general relativity.

Discrete Groups, Symmetric Spaces, and Global Holonomy

Symmetric Spaces with Conformal Symmetry

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a group-invariant metric and connection, and serves as the model space for a new conformal gauge theory. ∗Electronic-mail: [email protected]