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

Corro Tapia, Diego and Galaz García, Fernando 2020. Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions. Proceedings of the American Mathematical Society 148 (7) , pp. 3087-3097. 10.1090/proc/14961

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Abstract

We show that, for each $n>1$, 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 actionof cohomogeneity two supportsmetrics with positive Ricci curvature invariant under a circle or$T^2$-action, respectively.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	American Mathematical Society
ISSN:	0002-9939
Last Modified:	02 Nov 2023 15:30
URI:	https://orca.cardiff.ac.uk/id/eprint/162205

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