Einstein manifolds of non-negative sectional curvature and entropy

Details Einstein manifolds of non-negative sectional curvature and entropy Einstein manifolds of non-negative sectional curvature and entropy

2000-02-22

arxiv.org/abs/math/0002188v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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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