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arXiv · 1402.7255

On a generalized conjecture of Hopf with symmetry

Manuel Amann·Lee Kennard
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Abstract

A famous conjecture of Hopf is that the product of the two-dimensional sphere with itself does not admit a Riemannian metric with positive sectional curvature. More generally, one may conjecture that this holds for any nontrivial product. We provide evidence for this generalized conjecture in the presence of symmetry.

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Manuel Amann, Lee Kennard. 2014-02-28. On a generalized conjecture of Hopf with symmetry. https://doi.org/10.1112/s0010437x16008150

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