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

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

2010-10-22

arxiv.org/abs/1010.4620v2

Mathematics

Differential Geometry

20 pages, minor changes

Scientific paper

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.

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