Nonnegatively curved fixed point homogeneous manifolds in low dimensions

2009/11/06 by Fernando Galaz‐García, Galaz-Garcia, Fernando
Mathematics · Physics and Astronomy · #53C20 #53C21 #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.0911.1254

openalex publication_date 2009/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set M^G. We say that M is fixed-point homogeneous if G acts transitively on a normal sphere to some component of M^G. Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure.

Citations

• Ricci flow with surgery on three-manifolds

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