On the moduli space of nonnegatively curved metrics on Milnor spheres

2017/12/23 by Anand Dessai, Dessai, Anand
Mathematics · #53C20 #57R55 #58D27 #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.1712.08821

openalex publication_date 2017/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a Milnor sphere or, more generally, the total space of a linear S³-bundle over S⁴ with H⁴(M;ℚ)=0. We show that the moduli space of metrics of nonnegative sectional curvature on M has infinitely many path components. The same holds true for the moduli space of metrics of positive Ricci curvature on M.

Related

• Moduli space of non-negative sectional or positive Ricci curvature metrics on sphere bundles over spheres and their quotients
• The moduli Space of nonnegatively curved metrics on quotients of S²× S³ by involutions
• Moduli space of metrics of nonnegative sectional or positive Ricci curvature on Brieskorn quotients in dimension 5
• Moduli space of metrics of nonnegative sectional or positive Ricci\n curvature on homotopy real projective spaces
• Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms