Einstein manifolds of non-negative sectional curvature and entropy
Differential Geometry
2007-05-23 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.math/0002188,
title = {Einstein manifolds of non-negative sectional curvature and entropy},
author = {Gabriel Paternain and Jimmy Petean},
journal= {arXiv preprint arXiv:math/0002188},
year = {2007}
}
Comments
13 pages