Gallot-Tanno theorem for pseudo-Riemannian metrics and a proof that decomposable cones over closed complete pseudo-Riemannian manifolds do not exist

TL;DR

This paper extends the Gallot-Tanno theorem to pseudo-Riemannian metrics and uses it to prove that decomposable cones over complete closed pseudo-Riemannian manifolds cannot exist.

Contribution

The paper generalizes a classical theorem to pseudo-Riemannian metrics and provides a new proof for the non-existence of decomposable cones over certain manifolds.

Findings

Generalization of Gallot-Tanno theorem to pseudo-Riemannian metrics

Proof that decomposable cones over complete closed pseudo-Riemannian manifolds do not exist

Reproves recent non-existence result using the generalized theorem

Abstract

We generalize for pseudo-Riemannian metrics a classical result of Gallot and Tanno and use it to reprove a recent result of Alekseevsky, Cortes, Galaev and Leistner that decomposable cones over complete closed pseudo-Riemannian manifolds do not exist.