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Positive Intermediate Ricci Curvature with Maximal Symmetry Rank

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Abstract

Generalizing the foundational work of Grove and Searle, the second author proved upper bounds on the ranks of isometry groups of closed Riemannian manifolds with positive intermediate Ricci curvature and established some topological rigidity results in the case of maximal symmetry rank and positive second intermediate Ricci curvature. Here, we recover even stronger topological rigidity, including results for higher intermediate Ricci curvatures and for manifolds with non-trivial fundamental groups.

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Notes

  1. This notion of positive intermediate Ricci curvature should not be confused with k-positive Ricci curvature as defined in [76]; see also [8, 78].

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Acknowledgements

The authors would like to thank William Wylie, Jason DeVito, Marco Radeschi, and Fernando Galaz-García for helpful discussions, along with Jason DeVito and Philipp Reiser for suggestions on a previous version of this article. We also thank the referees for their comments to improve the exposition. The first author was funded by NSF Grant DMS-2005280 and Simons Foundation Award MPTSM-00002791, and the second author was funded by NSF Award DMS-2202826.

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  1. Department of Mathematics, Syracuse University, Syracuse, NY, USA

    Lee Kennard & Lawrence Mouillé

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Kennard, L., Mouillé, L. Positive Intermediate Ricci Curvature with Maximal Symmetry Rank. J Geom Anal 34, 129 (2024). https://doi.org/10.1007/s12220-024-01575-z

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