Geodesic
The nonembeddability of complete $q$-metrics of negative curvature in a class of weakly nonregular surfaces
Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 83-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper it is proved that a regular complete two-dimensional Riemainnian metric $ds^2$, having curvature $K<0$ subject to the condition $\sup|\frac\partial{\partial s}(|K|^{1/2})|<+\infty$, cannot be embedded in $R^3$ in the class of smooth surfaces regular except at a number of isolated points. The result is extended to metrics with singular points. Bibliography: 12 titles. 
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È. R. Rozendorn. The nonembeddability of complete $q$-metrics of negative curvature in a class of weakly nonregular surfaces. Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 83-92. http://geodesic.mathdoc.fr/item/SM_1972_18_1_a4/

[1] A. D. Aleksandrov, Vnutrennyaya geometriya vypuklykh poverkhnostei, Gostekhizdat, Moskva–Leningrad, 1948

[2] N. V. Efimov, “Vozniknovenie osobennostei na poverkhnostyakh otritsatelnoi krivizny”, Matem. sb., 64(106) (1964), 286–320 | MR | Zbl

[3] N. V. Efimov, “Poverkhnosti s medlenno izmenyayuscheisya otritsatelnoi kriviznoi”, Uspekhi matem. nauk, XXI:5(131) (1966), 3–58 | MR

[4] N. V. Efimov, “Differentsialnye priznaki gomeomorfnosti nekotorykh otobrazhenii s primeneniem v teorii poverkhnostei”, Matem. sb., 76(118) (1968), 499–512 | MR | Zbl

[5] V. A. Zalgaller, “O vozmozhnykh osobennostyakh gladkikh poverkhnostei”, Vestnik LGU, seriya matem., mekh., astron., 2:7 (1962), 71–77 | MR | Zbl

[6] N. X. Keiper, “O $C^1$-izometrichnykh vlozheniyakh”, Matematika, 1:2 (1957), 17–28

[7] D. Nesh, “$C^1$-izometrichnye vlozheniya”, Matematika, 1:2 (1957), 3–16

[8] E. R. Rozendorn, “O polnykh poverkhnostyakh otritsatelnoi krivizny $K\leqslant-1$ v evklidovykh prostranstvakh $E_3$ i $E_4$”, Matem. sb., 58(100) (1962), 453–475 | MR

[9] E. R. Rozendorn, “Issledovanie osnovnykh uravnenii teorii poverkhnostei v asimptoticheskikh koordinatakh”, Matem. sb., 70(112) (1966), 490–507 | MR | Zbl

[10] E. R. Rozendorn, “Slabo neregulyarnye poverkhnosti otritsatelnoi krivizny”, Uspekhi matem. nauk, XXI:5(131) (1966), 59–416 | MR

[11] Ph. Hartman, “On the local uniqeness of geodesies”, Amer. J. Math., 72:4 (1950), 723–730 | DOI | MR | Zbl

[12] Ph. Hartman, “On geodesic coordinates”, Amer. J. Math., 73:3 (1951), 949–954 | DOI | MR | Zbl