Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Corro - F. Galaz-Garcia

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

created by corro on 20 Jan 2022



Inserted: 20 jan 2022
Last Updated: 20 jan 2022

Year: 2016

ArXiv: 1609.06125 PDF


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.

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