Metrics of constant negative scalar-Weyl curvature

Giovanni Catino

Metrics of constant negative scalar-Weyl curvature

Differential Geometry 2021-01-20 v1

Authors: Giovanni Catino

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.

Keywords

constant negative scalar-weyl curvature closed manifold riemannian metric scalar curvature weyl curvature topological obstruction aubin construction

Cite

@article{arxiv.2101.07572,
  title  = {Metrics of constant negative scalar-Weyl curvature},
  author = {Giovanni Catino},
  journal= {arXiv preprint arXiv:2101.07572},
  year   = {2021}
}

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