Collapsed 5-manifolds with pinched positive sectional curvature

Fuquan Fang, Xiaochun Rong

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Let M be a closed 5-manifold of pinched curvature 0 < δ ≤ secM ≤ 1. We prove that M is homeomorphic to a spherical space form if one of the following conditions holds: (i)The center of the fundamental group has index ≥ w (δ), a constant depending on δ;(ii)δ = frac(1, 4 (1 + 10- 6)2) and the fundamental group is a non-cyclic group of order ≥C, a constant;(iii)The volume is less than ε{lunate} (δ) and the fundamental group is either isomorphic to a spherical 5-space group or has an odd order, and it has a center of index ≥w, a constant.

Original languageEnglish (US)
Pages (from-to)830-860
Number of pages31
JournalAdvances in Mathematics
Issue number3
StatePublished - Jun 20 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Collapsing
  • Isometric torus action
  • Positive pinching


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