Negatively pinched $3$-manifolds admit hyperbolic metrics
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- by Dale N. Skinner PDF
- Proc. Amer. Math. Soc. 129 (2001), 3069-3077 Request permission
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.References
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- Richard S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982), no. 2, 255–306. MR 664497
- Maung Min-Oo, Almost Einstein manifolds of negative Ricci curvature, J. Differential Geom. 32 (1990), no. 2, 457–472. MR 1072914
- Rugang Ye, Ricci flow, Einstein metrics and space forms, Trans. Amer. Math. Soc. 338 (1993), no. 2, 871–896. MR 1108615, DOI 10.1090/S0002-9947-1993-1108615-3
Additional Information
- Dale N. Skinner
- Affiliation: 4746 19th Ave NE, #5, Seattle, Washington 98105
- Email: skinner@math.washington.edu
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3069-3077
- MSC (2000): Primary 53C20; Secondary 53C21, 53C25, 58J60
- DOI: https://doi.org/10.1090/S0002-9939-01-05899-3
- MathSciNet review: 1840113