Holonomy of tame Weyl Structures

Florin Belgun (1) , Andrei Moroianu (2)

1 Institut für Mathematik [Berlin]
2 CMLS - Centre de Mathématiques Laurent Schwartz

A Weyl structure on a compact conformal manifold is not complete in general. If, however, the life-time of incomplete geodesics can be controlled on compact subsets of the tangent bundle, the Weyl connection is called tame. We prove that every closed, non-exact, tame Weyl structure on a compact conformal manifold is either flat, or has irreducible holonomy, generalizing a classical statement for Riemannian cone metrics by S. Gallot.

Mots clés: Weyl structures; reducible holonomy; cone metrics; tame connections

Domaines: Géométrie différentielle [math.DG]

Florin Belgun, Andrei Moroianu. Holonomy of tame Weyl Structures. 2009. ⟨hal-00405115⟩