Einstein manifolds of non-negative sectional curvature and entropy

Gabriel Paternain; Jimmy Petean

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arXiv · math/0002188

Einstein manifolds of non-negative sectional curvature and entropy

Gabriel Paternain·Jimmy Petean

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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.

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BibTeX RIS

Gabriel Paternain, Jimmy Petean. 2000-02-22. Einstein manifolds of non-negative sectional curvature and entropy. https://arxiv.org/abs/math/0002188

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