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Mathematical Research Letters
Volume 30 (2023)
Number 2
Metrics of constant negative scalar-Weyl curvature
Pages: 319 – 340
DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n2.a2
Author
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, $R + t {\lvert W \rvert}, t \in \mathbb{R}$. In particular, there are no topological obstructions for metrics with $\varepsilon$-pinched Weyl curvature and negative scalar curvature.
Received 26 February 2021
Received revised 27 August 2021
Accepted 19 October 2021
Published 13 September 2023