Classification of Cohomogeneity One Manifolds in Low Dimensions

2007/12/09 by Corey A. Hoelscher, Hoelscher, Corey A. · 2 citations
Computer Science · Mathematics · #53C20 #57S15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0712.1327

openalex publication_date 2007/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A cohomogeneity one manifold is a manifold with the action of a compact Lie group, whose quotient is one dimensional. Such manifolds are of interest in Riemannian geometry, in the context of nonnegative sectional curvature, as well as in other areas of geometry and in physics. In this paper we classify compact simply connected cohomogeneity one manifolds in dimensions 5, 6 and 7. We also show that all such manifolds admit metrics of nonnegative sectional curvature, with the possible exception of two families of manifolds.

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• Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions
• On steady and expanding Ricci solitons with asymptotic symmetries

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