On the completions of the spaces of metrics on an open manifold
type: Item
instance of: scholarly article
title: On the completions of the spaces of metrics on an open manifold
zbMATH Open document ID: 0864.58005
DOI: 10.1007/BF03322230
author: Gorm Salomonsen
published in: Results in Mathematics
publication date: 1996-08-27T00:00:00Z
review text: For a smooth manifold \(X\) the function \(d_0\) defined by: \[ d_0(g,g')=\sup_{x\in X}\sup_{Y\in T_x X-\{0\}} {|g_x(Y,Y)-g_x'(Y,Y)|\over g_x(Y,Y)+g_x'(Y,Y)} \] is a complete metric on the space of complete \(C^0\) metrics on \(X\). This metric is then used to show that a space of strictly positive definite smooth metrics with a natural uniform structure is complete.
Mathematics Subject Classification ID: 58D17
Mathematics Subject Classification ID: 54E50
zbMATH DE Number: 920817
zbMATH Keywords: space of metrics
zbMATH Keywords: complete metric space
reviewed by: David B. Gauld
MaRDI profile type: Publication
cites work: Spaces of Riemannian metrics on open manifolds
description: scientific article; zbMATH DE number 920817