Geodesic
Some formulas arising in conformal mapping of a Riemann space onto a Euclidean space and corollaries following from them
Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 513-520 Cet article a éte moissonné depuis la source Math-Net.Ru

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Formulas are derived for transforming the total and mean curvature of a surface $R_2$ in a Riemann space $R_3$ under conformal mapping of $R_3$ onto a Euclidean space. 
@article{MZM_1969_6_5_a0,
     author = {V. T. Fomenko},
     title = {Some formulas arising in conformal mapping of {a~Riemann} space onto {a~Euclidean} space and corollaries following from them},
     journal = {Matemati\v{c}eskie zametki},
     pages = {513--520},
     year = {1969},
     volume = {6},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a0/}
}
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V. T. Fomenko. Some formulas arising in conformal mapping of a Riemann space onto a Euclidean space and corollaries following from them. Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 513-520. http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a0/