Almost positively curved generalized Eschenburg spaces

2025/11/21 by DeVito, Jason, West, Joan
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2511.17751

Abstract

In each dimension of the form 4n-1 with n≥ 3, we construct infinitely many new examples of manifolds admitting metrics with positive sectional curvature almost everywhere. In addition, we show that if n≥ 6, infinitely many of our examples are not homotopy equivalent to any homogeneous space, providing the first infinite family of such examples.

Citations

• Curvature on Eschenburg spaces
• Cohomogeneity one manifolds with quasipositive curvature
• Three new almost positively curved manifolds
• Almost positive curvature on the Gromoll-Meyer sphere
• Flats in Riemannian Submersions from Lie Groups
• Quasi-positive curvature on homogeneous bundles

Related

• Curvature on Eschenburg spaces
• Three new almost positively curved manifolds
• Revisiting homogeneous spaces with positive curvature
• A note on totally geodesic embeddings of Eschenburg spaces into Bazaikin\n spaces
• Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry