Journal of Differential Geometry

Regenerating Singular Hyperbolic Structures from Sol

Michael Heusener, Joan Porti, and Eva Suárez


Let M be a torus bundle over S1 with an orientation preserving Anosov monodromy. The manifold M admits a geometric structure modeled on Sol. We prove that the Sol structure can be deformed into singular hyperbolic cone structures whose singular locus Σ ⊂ M is the mapping torus of the fixed point of the monodromy.

The hyperbolic cone metrics are parametred by the cone angle α in the interval (0, 2π). When α → 2π, the cone manifolds collapse to the basis of the fibration S1, and they can be rescaled in the direction of the fibers to converge to the Sol manifold.

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J. Differential Geom., Volume 59, Number 3 (2001), 439-478.

First available in Project Euclid: 20 July 2004

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Heusener, Michael; Porti, Joan; Suárez, Eva. Regenerating Singular Hyperbolic Structures from Sol. J. Differential Geom. 59 (2001), no. 3, 439--478. doi:10.4310/jdg/1090349448.

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