Open Access
November, 2001 Regenerating Singular Hyperbolic Structures from Sol
Michael Heusener, Joan Porti, Eva Suárez
J. Differential Geom. 59(3): 439-478 (November, 2001). DOI: 10.4310/jdg/1090349448


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.


Download Citation

Michael Heusener. Joan Porti. Eva Suárez. "Regenerating Singular Hyperbolic Structures from Sol." J. Differential Geom. 59 (3) 439 - 478, November, 2001.


Published: November, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1042.57008
MathSciNet: MR1916952
Digital Object Identifier: 10.4310/jdg/1090349448

Rights: Copyright © 2001 Lehigh University

Vol.59 • No. 3 • November, 2001
Back to Top