TITLE

The metric geometry of the manifold of Riemannian metrics over a closed manifold

AUTHOR(S)
Clarke, Brian
PUB. DATE
November 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2010, Vol. 39 Issue 3/4, p533
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We prove that the L Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space structure. As the L metric is a weak Riemannian metric, this fact does not follow from general results. In addition, we prove several results on the exponential mapping and distance function of a weak Riemannian metric on a Hilbert/Fréchet manifold. The statements are analogous to, but weaker than, what is known in the case of a Riemannian metric on a finite-dimensional manifold or a strong Riemannian metric on a Hilbert manifold.
ACCESSION #
54354944

 

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