Positive intermediate curvatures and Ricci flow

2023/03/15 by David González-Álvaro, Masoumeh Zarei, González-Álvaro, David +1 · 1 citation
Mathematics · Physics and Astronomy · #53C21 (Primary) #53E20 (Secondary) #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.2303.08641

openalex publication_date 2023/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, for any n≥ 2, there exists a homogeneous space of dimension d=8n-4 with metrics of Ric_(d)/(2)-5>0 if n≠ 3 and Ric₆>0 if n=3 which evolve under the Ricci flow to metrics whose Ricci tensor is not (d-4)-positive. Consequently, Ricci flow does not preserve a range of curvature conditions that interpolate between positive sectional and positive scalar curvature. This extends a theorem of Böhm and Wilking in the case of n=2.

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