Journal of Differential Geometry

Regenerating Singular Hyperbolic Structures from Sol

Michael Heusener, Joan Porti, and Eva Suárez

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090349448

Digital Object Identifier
doi:10.4310/jdg/1090349448

Mathematical Reviews number (MathSciNet)
MR1916952

Zentralblatt MATH identifier
1042.57008

Citation

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. https://projecteuclid.org/euclid.jdg/1090349448


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