Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 006, 17 pages      arXiv:2211.14610      https://doi.org/10.3842/SIGMA.2025.006

Positive Intermediate Ricci Curvature on Fibre Bundles

Philipp Reiser a and David J. Wraith b
a) Department of Mathematics, University of Fribourg, Switzerland
b) Department of Mathematics and Statistics, National University of Ireland Maynooth, Maynooth, County Kildare, Ireland

Received August 15, 2024, in final form January 20, 2025; Published online January 23, 2025

Abstract
We prove a canonical variation-type result for submersion metrics with positive intermediate Ricci curvatures. This can then be used in conjunction with surgery techniques to establish the existence of metrics with positive intermediate Ricci curvatures on a wide range of examples which had previously only been known to admit positive Ricci curvature, such as highly connected manifolds and exotic spheres. Further, we extend results of the second author on the moduli space of metrics with positive Ricci curvature to positive intermediate Ricci curvatures.

Key words: positive intermediate Ricci curvature; fibre bundle; plumbing; homotopy sphere; moduli space.

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