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Literature Cited
S. Z. Shefel', “Completely regular isometric immersions in a Euclidean space,” Sib. Mat. Zh.,11, No. 2, 442–460 (1970).
E. Calabi and P. Hartman, “On the smoothness of isometrics,” Duke Math. J.,37, No. 4, 741–751 (1970).
A. D. Aleksandrov and V. V. Zalgaller, “Two-dimenional manifolds of bounded curvature,” Tr. Mat. Inst. Akad. Nauk SSSR,63, 262 (1962).
Yu. G. Reshetnyak, “Isothermal coordinate in manifold of bounded curvature,” Sib. Mat. Zh.,1, No. 1, 86–116 (1960); No. 2, 248–276 (1960).
Yu. G. Reshetnyak, “The turning of a curve in a manifold of bounded curvature with an isothermal linear mtric element,” Sib. Mat. Zh.,4, No. 4, 870–911 (1963).
Yu. G. Reshetnyak, “Study of manifolds of bounded curvature by means of isothermal coordinates,” Izv. Sib. Otd. Akad. Nauk SSSR, No. 10, 15–28 (1959).
L. P. Eisenhart, Riemannian Geometry, Princeton Univ. Press.
O. A. Ladyzhenskaya and I. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).
Additional information
Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 20, No. 2, pp. 397–401, March–April, 1979.
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Shefel', S.Z. Conformal correspondence of metrics and smoothnes of isometric immersions. Sib Math J 20, 284–287 (1979). https://doi.org/10.1007/BF00970036
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DOI: https://doi.org/10.1007/BF00970036