On parallel and symmetric 2-tensorfields on cones over pseudo-Riemannian manifolds.

Pierre Mounoud (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric $2$-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and decomposable cases we provide a classification. In the nilpotent case, we are able to describe completely only a dense open subset of the manifold. To conclude, we give examples with non-constant curvature in the nilpotent case.

Domaines: Géométrie différentielle [math.DG]

Pierre Mounoud. On parallel and symmetric 2-tensorfields on cones over pseudo-Riemannian manifolds.. Communications in Analysis and Geometry, 2012, 20 (1), pp.203-233. ⟨hal-00528147v2⟩