## D. Corro - F. Galaz-Garcia

# Positive Ricci curvature on simply-connected manifolds with
cohomogeneity-two torus actions

created by corro on 20 Jan 2022

[

BibTeX]

*preprint*

**Inserted:** 20 jan 2022

**Last Updated:** 20 jan 2022

**Year:** 2016

**Abstract:**

A gap in the proof of the main result in reference 1 in our original
submission propagated into the constructions presented in the first version of
our manuscript. In this version we give an alternative proof for the existence
of Riemannian metrics with positive Ricci curvature on an infinite subfamily of
closed, simply-connected smooth manifolds with a cohomogeneity two torus action
and recover some of our original results.
Namely, we show that, for each $n\geqslant 1$, there exist infinitely many
spin and non-spin diffeomorphism types of closed, smooth, simply-connected
$(n+4)$-manifolds with a smooth, effective action of a torus $T^{n+2}$ and a
metric of positive Ricci curvature invariant under a $T^{n}$-subgroup of
$T^{n+2}$. As an application, we show that every closed, smooth,
simply-connected $5$- and $6$-manifold admitting a smooth, effective torus
action of cohomogeneity two supports metrics with positive Ricci curvature.