Calculus of Variations and Geometric Measure Theory

G. Catino

Metrics of constant negative scalar-Weyl curvature

created by catino on 19 Jan 2021
modified on 22 Oct 2023

[BibTeX]

Published Paper

Inserted: 19 jan 2021
Last Updated: 22 oct 2023

Journal: Math. Res. Lett.
Volume: 30
Number: 2
Pages: 319-340
Year: 2023

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.


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