Ricci-Positive Metrics on Connected Sums of Projective Spaces
| Autor: | Bradley Lewis Burdick |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Betti number 010102 general mathematics Dimension (graph theory) Geometric Topology (math.GT) 01 natural sciences Mathematics - Geometric Topology 53C20 53C25 Computational Theory and Mathematics Differential Geometry (math.DG) 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology Sectional curvature Projective plane Mathematics::Differential Geometry 0101 mathematics Projective test Analysis Ricci curvature Mathematics |
| DOI: | 10.48550/arxiv.1705.05055 |
| Popis: | It is a well known result of Gromov that all manifolds of a given dimension with positive sectional curvature are subject to a universal bound on the sum of their Betti numbers. On the other hand, there is no such bound for manifolds with positive Ricci curvature: indeed, Perelman constructed positive Ricci metrics on arbitrary connected sums of complex projective planes. In this paper, we revisit and extend Perelman's techniques to construct positive Ricci metrics on arbitrary connected sums of complex, quaternionic, and octonionic projective spaces in every dimension. Comment: Final Version. 25 pages, 11 figures. Accepted for publication in Differential Geometry and its Applications. See author's webpage for technical appendices |
| Databáze: | OpenAIRE |
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