Mathematics

A quasi-Fuchsian group is a deformation of a Fuchsian group such that the quotient space is homeomorphic to a surface cross an interval. The quotient space is called a quasi-Fuchsian manifold.

If a quasi-Fuchsian manifold contains an embedded surface with the principal curvatures in the range of (-1,1), such a manifold admits a foliation of parallel surfaces. The Teichmuller distance between the two components of the conformal boundary of the manifold is related to principle curvatures of the embedded surface.