Infinite families of manifolds of positive k^{\rm th}-intermediate Ricci curvature with k small

2020/12/21 by Miguel Domínguez-Vázquez, Domínguez-Vázquez, Miguel, David González-Álvaro +3 · 2 citations
Mathematics · Physics and Astronomy · #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.2012.11640

openalex publication_date 2020/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

Positive k^{\rm th}-intermediate Ricci curvature on a Riemannian n-manifold, to be denoted by Ric_k > 0, is a condition that interpolates between positive sectional and positive Ricci curvature (when k =1 and k=n-1 respectively). In this work, we produce many examples of manifolds of Ric_k > 0 with k small by examining symmetric and normal homogeneous spaces, along with certain metric deformations of fat homogeneous bundles. As a consequence, we show that every dimension n≥ 7 congruent to 3 mod 4 supports infinitely many closed simply connected manifolds of pairwise distinct homotopy type, all of which admit homogeneous metrics of Ric_k > 0 for some k 0 with k≤ n/2, but do not admit metrics of positive sectional curvature.

Citations

• Manifolds all of whose Geodesics are Closed
• Examples of Riemannian Manifolds with non-negative sectional curvature
• Compact Homogeneous Riemannian Manifolds with Strictly Positive Curvature
• An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures
• Restrictions on Submanifolds via Focal Radius Bounds
• The flavour of intermediate Ricci and homotopy when studying\n submanifolds of symmetric spaces

Cited by

• Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions
• On Hopf's conjecture and positive second intermediate Ricci curvature

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