Moduli space of metrics of nonnegative sectional or positive Ricci\n curvature on homotopy real projective spaces

2019/02/24 by Anand Dessai, Dessai, Anand, David González-Álvaro +1
Mathematics · Physics and Astronomy · #19K56 #53C20 #53C27 #57R55 #58D27 #58J28 #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.1902.08919

openalex publication_date 2019/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the moduli space of metrics of nonnegative sectional curvature\non every homotopy mathbb R P⁵ has infinitely many path components. We\nalso show that in each dimension 4k+1 there are at least 2^2k homotopy\n mathbb R P^4k+1s of pairwise distinct oriented diffeomorphism type for\nwhich the moduli space of metrics of positive Ricci curvature has infinitely\nmany path components. Examples of closed manifolds with finite fundamental\ngroup with these properties were known before only in dimensions 4k+3\≥ 7.\n

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