## Geometry & Topology

### A formal Riemannian structure on conformal classes and uniqueness for the $\sigma_2$–Yamabe problem

#### Abstract

We define a new formal Riemannian metric on a conformal classes of four-manifolds in the context of the $σ 2$–Yamabe problem. Exploiting this new variational structure we show that solutions are unique unless the manifold is conformally equivalent to the round sphere.

#### Article information

Source
Geom. Topol., Volume 22, Number 6 (2018), 3501-3573.

Dates
Revised: 29 September 2017
Accepted: 10 November 2017
First available in Project Euclid: 29 September 2018

https://projecteuclid.org/euclid.gt/1538186742

Digital Object Identifier
doi:10.2140/gt.2018.22.3501

Mathematical Reviews number (MathSciNet)
MR3858769

Zentralblatt MATH identifier
06945131

#### Citation

Gursky, Matthew; Streets, Jeffrey. A formal Riemannian structure on conformal classes and uniqueness for the $\sigma_2$–Yamabe problem. Geom. Topol. 22 (2018), no. 6, 3501--3573. doi:10.2140/gt.2018.22.3501. https://projecteuclid.org/euclid.gt/1538186742

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