Exotic smoothings of hyperbolic manifolds which do not support pinched negative curvature

Farrell, F. T.; Jones, L. E.

doi:10.1090/S0002-9939-1994-1203985-6

Exotic smoothings of hyperbolic manifolds which do not support pinched negative curvature
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by F. T. Farrell and L. E. Jones PDF

Proc. Amer. Math. Soc. 121 (1994), 627-630 Request permission

Abstract:

Constructed in this note are examples of topological manifolds M supporting at least two distinct smooth structures ${\mathcal {M}_1}$ and ${\mathcal {M}_2}$, where ${\mathcal {M}_1}$ is a complete, finite volume, real hyperbolic manifold, while ${\mathcal {M}_2}$ cannot support a complete, finite volume, pinched negatively curved Riemannian metric.

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