Journal of Differential Geometry
- J. Differential Geom.
- Volume 93, Number 2 (2013), 203-268.
The completion of the manifold of Riemannian metrics
We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finitedimensional, orientable manifold with respect to a natural metric called the $L^2$ metric. The primary motivation for studying this problem comes from Teichmüller theory, where similar considerations lead to a completion of the well-known Weil-Petersson metric. We give an application of the main theorem to the completions of Teichmüller space with respect to a class of metrics that generalize the Weil-Petersson metric.
J. Differential Geom., Volume 93, Number 2 (2013), 203-268.
First available in Project Euclid: 25 February 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Clarke, Brian. The completion of the manifold of Riemannian metrics. J. Differential Geom. 93 (2013), no. 2, 203--268. doi:10.4310/jdg/1361800866. https://projecteuclid.org/euclid.jdg/1361800866