Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Authors: Diego Corro and Fernando Galaz-García
Journal: Proc. Amer. Math. Soc. 148 (2020), 3087-3097
MSC (2010): Primary 53C20, 57S15
DOI: https://doi.org/10.1090/proc/14961
Published electronically: March 31, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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 invariant under a circle or $ T^2$-action, respectively.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C20, 57S15

Retrieve articles in all journals with MSC (2010): 53C20, 57S15


Additional Information

Diego Corro
Affiliation: Institut für Algebra und Geometrie, Karlsruher Institut für Technologie (KIT), 76131 Karlsruhe, Germany
Email: diego.corro@partner.kit.edu

Fernando Galaz-García
Affiliation: Institut für Algebra und Geometrie, Karlsruher Institut für Technologie (KIT), 76131 Karlsruhe, Germany
Address at time of publication: Department of Mathematical Sciences, Durham University, Durham, United Kingdom
Email: galazgarcia@kit.edu; fernando.galaz-garcia@durham.ac.uk

DOI: https://doi.org/10.1090/proc/14961
Keywords: Cohomogeneity two, torus action, positive Ricci curvature, symmetry rank
Received by editor(s): September 19, 2019
Received by editor(s) in revised form: December 4, 2019
Published electronically: March 31, 2020
Additional Notes: The first author was supported by CONACYT-DAAD (scholarship number 409912).
The second author was supported by the DFG (grant GA 2050 2-1, SPP2026 “Geometry at Infinity”).
Both authors were supported by the DFG (281869850, RTG 2229 “Asymptotic Invariants and Limits of Groups and Spaces”).
Communicated by: Guofang Wei
Article copyright: © Copyright 2020 American Mathematical Society