Einstein manifolds of non-negative sectional curvature and entropy
Abstract
We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieved by combining the classical Morse theory of the loop space with a new upper bound for the topological entropy of the geodesic flow in terms of the curvature tensor.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- February 2000
- DOI:
- 10.48550/arXiv.math/0002188
- arXiv:
- arXiv:math/0002188
- Bibcode:
- 2000math......2188P
- Keywords:
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- Differential Geometry;
- Dynamical Systems;
- 53C25
- E-Print:
- 13 pages