The hopf conjecture for manifolds with abelian group actions

Xiaochun Rong, S. U. Xiaole

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Let M be a closed even n-manifold of positive sectional curvature on which a torus Tk acts isometrically. We show that if k ≥ n-4/8 (respectively, k > 1) for n ≠ 12 (respectively, n = 12), then the Euler characteristic of each Tk-fixed point component is positive. This implies that the Euler characteristic of M is positive. We also extend this result to an isometric elementary p-group ℤpk-action on a closed manifold of positive sectional curvature.

Original languageEnglish (US)
Pages (from-to)121-136
Number of pages16
JournalCommunications in Contemporary Mathematics
Issue number1
StatePublished - Feb 2005

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Euler characteristics
  • Hopf conjecture
  • Positive curvature
  • Torus action


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