Metric spaces of diffeomorphisms
Let V be a connected n-dimensional Riemannian \(C^ 2\)-manifold, let \(\rho\) (.,.) be the distance on V induced by its metric and let S be the set of all \(C^ 1\)-diffeomorphisms mapping V onto V. For \(j\in S\) the author introduces the set \(S_ j=\{f\in S:\) sup \(\rho\) (fx,jx)\(<\infty \}\). He defines two distance functions on each \(S_ j\) and shows that they are metrics.
scientific article; zbMATH DE number 3947243