Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions

2025/07/23 by Elahe Khalili Samani, Samani, Elahe Khalili, Lawrence Mouillé +1
Mathematics · Physics and Astronomy · #53C20 #57S15 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2507.17920

openalex publication_date 2025/07/23 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We explore existence of invariant metrics with positive intermediate Ricci curvature on closed, low-dimensional cohomogeneity one manifolds. For a certain cohomogeneity one Spin(4)-action on S³ × ℂP², we construct an invariant metric with positive 4th-intermediate Ricci curvature and show it cannot admit an invariant metric with positive 3rd-intermediate Ricci curvature. We further establish similar symmetry obstructions to positive curvature for S³ × S³, S³ × S⁴, and several families of cohomogeneity one manifolds.

Citations

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• Positive intermediate Ricci curvature on products of homogeneous spaces
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• G-manifolds with positive Ricci curvature and many isolated singular orbits
• Positive intermediate curvatures and Ricci flow