Open Access
February 2013 The completion of the manifold of Riemannian metrics
Brian Clarke
J. Differential Geom. 93(2): 203-268 (February 2013). DOI: 10.4310/jdg/1361800866


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.


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Brian Clarke. "The completion of the manifold of Riemannian metrics." J. Differential Geom. 93 (2) 203 - 268, February 2013.


Published: February 2013
First available in Project Euclid: 25 February 2013

zbMATH: 1183.53003
MathSciNet: MR3024306
Digital Object Identifier: 10.4310/jdg/1361800866

Rights: Copyright © 2013 Lehigh University

Vol.93 • No. 2 • February 2013
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