preprint
Inserted: 17 oct 2023
Last Updated: 17 oct 2023
Year: 2021
Abstract:
Extending Aubin's construction of metrics with constant negative scalar
curvature, we prove that every $n$-dimensional closed manifold admits a
Riemannian metric with constant negative scalar-Weyl curvature, that is
$R+t
W
, t\in\mathbb{R}$. In particular, there are no topological obstructions
for metrics with $\varepsilon$-pinched Weyl curvature and negative scalar
curvature.