preprint
Inserted: 17 oct 2023
Last Updated: 17 oct 2023
Year: 2022
Abstract:
In this paper, using special metric deformations introduced by Aubin, we construct Riemannian metrics satisfying non-vanishing conditions concerning the Weyl tensor, on every closed manifolds. In particular, in dimension four, we show that there are no topological obstructions for the existence of metrics with non-vanishing Bach tensor.