# Metrics of constant negative scalar-Weyl curvature

created by catino on 19 Jan 2021

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Preprint

Inserted: 19 jan 2021
Last Updated: 19 jan 2021

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.