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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Negatively pinched $3$-manifolds admit hyperbolic metrics


Author: Dale N. Skinner
Journal: Proc. Amer. Math. Soc. 129 (2001), 3069-3077
MSC (2000): Primary 53C20; Secondary 53C21, 53C25, 58J60
Published electronically: February 22, 2001
MathSciNet review: 1840113
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Abstract:

We show that any compact 3-manifold carrying a metric with sufficiently pinched negative Ricci curvature admits a hyperbolic metric. This proof is a corrected version of the proof first suggested by Maung Min-Oo. The key insight in this new proof is that the error in Min-Oo's paper does not occur if the type $(4,0)$ curvature is considered instead of the type $(3,1)$ curvature.


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Additional Information

Dale N. Skinner
Affiliation: 4746 19th Ave NE, #5, Seattle, Washington 98105
Email: skinner@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05899-3
PII: S 0002-9939(01)05899-3
Received by editor(s): March 27, 1997
Received by editor(s) in revised form: February 17, 2000
Published electronically: February 22, 2001
Additional Notes: Research supported in part by National Science Foundation grant DMS-9404107.
Communicated by: Christopher Croke
Article copyright: © Copyright 2001 American Mathematical Society