On a generalized conjecture of Hopf with symmetry

Manuel Amann, Lee Kennard

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A famous conjecture of Hopf states that does not admit a Riemannian metric with positive sectional curvature. In this article, we prove that no manifold product can carry a metric of positive sectional curvature admitting a certain degree of torus symmetry.

Original languageEnglish (US)
Pages (from-to)313-322
Number of pages10
JournalCompositio Mathematica
Issue number2
StatePublished - Feb 1 2017
Externally publishedYes


  • Euler characteristic
  • Hopf conjecture
  • positive curvature
  • torus symmetry

ASJC Scopus subject areas

  • Algebra and Number Theory


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