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

Corro, Diego; Galaz-García, Fernando

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 action of cohomogeneity two supports metrics with positive Ricci curvature invariant under a circle or T2-action, respectively.

Citation

Corro, D., & Galaz-García, F. (2020). Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions. Proceedings of the American Mathematical Society, 148(7), 3087-3097. https://doi.org/10.1090/proc/14961

• Journal Article Type: Article
• Acceptance Date: Dec 4, 2019
• Online Publication Date: Mar 31, 2020
• Publication Date: Jul 31, 2020
• Deposit Date: Jan 31, 2020
• Publicly Available Date: May 20, 2020
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 148
• Issue: 7
• Pages: 3087-3097
• DOI: https://doi.org/10.1090/proc/14961
• Related Public URLs: https://arxiv.org/abs/1609.06125