Immersions of locally euclidean and conformally flat metrics

The possibility of imbedding $n$-dimensional locally Euclidean metrics in the large in $\mathbf R^n$ is studied by means of the global inverse function theorem in the forms suggested by Hadamard, John, Levy and Plastock. The imbeddability of conformally Euclidean metrics is studied by means of a theorem of Zorich on the removability of an isolated singularity of a locally quasiconformal mapping.