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- Title
Positively curved Riemannian metrics with logarithmic symmetry rank bounds.
- Authors
Kennard, Lee
- Abstract
We prove an obstruction at the level of rational cohomology to the existence of positively curved metrics with large symmetry rank. The symmetry rank bound is logarithmic in the dimension of the manifold. As one application, we provide evidence for a generalized conjecture of H. Hopf, which states that no symmetric space of rank at least two admits a metric with positive curvature. Other applications concern product manifolds, connected sums, and manifolds with nontrivial fundamental group.
- Subjects
LAGRANGIAN mechanics; RIEMANNIAN geometry; GENERALIZED spaces; RIEMANNIAN metric; LOGARITHMIC functions; RIEMANNIAN manifolds; MATHEMATICAL symmetry
- Publication
Commentarii Mathematici Helvetici, 2014, Vol 89, Issue 4, p937
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/340