Cohomogeneity one manifolds with quasipositive curvature

2022/04/25 by Dennis Wulle, Wulle, Dennis · 1 citation
Mathematics · #53C21 (Primary) #57S25 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2204.11652

openalex publication_date 2022/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a classification of cohomogeneity one manifolds admitting an invariant metric with quasipositive sectional curvature except for two 7-dimensional families. The main result carries over almost verbatim from the classification results in positive curvature carried out by Verdiani and Grove, Wilking and Ziller. Three main tools used in the positively curved case that we generalized to quasipositively curved cohomogeneity one manifolds are Wilking's Chain Theorem, the classification of positively curved fixed point homogeneous manifolds by Grove and Searle and the Rank Lemma.

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• Almost positively curved generalized Eschenburg spaces

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