2006/08/30 by Luis A. Florit, Wolfgang Ziller, Florit, Luis +1
Mathematics · Physics and Astronomy · #53C20 #55R55 #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.math/0608745
openalex publication_date 2006/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study isometric circle actions on 7 dimensional positively curved Eschenburg spaces which are almost free, thus giving rise to orbifold fibrations of these spaces. This shows in particular that every known example of compact manifolds with positive sectional curvature is the total space of an orbifold fibration. We then study in detail the geometry of the singular locus and how to minimize it. As a consequence we obtain, for example, a six dimensional compact positively curved orbifold with only two singular points with orbifold groups Z2.