Geodesic
Immersions of locally euclidean and conformally flat metrics
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 467-478

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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. 
@article{SM_1992_73_2_a9,
     author = {V. A. Aleksandrov},
     title = {Immersions of locally euclidean and conformally flat metrics},
     journal = {Sbornik. Mathematics},
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     volume = {73},
     number = {2},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_73_2_a9/}
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V. A. Aleksandrov. Immersions of locally euclidean and conformally flat metrics. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 467-478. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a9/