Geodesic
Linearizability of holomorphic mappings of generating manifolds of codimension~2 in $\mathbf C^4$
Izvestiya. Mathematics , Tome 36 (1991) no. 3, pp. 655-667

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In this article we consider the problem of uniqueness of so-called normal coordinates for real-analytic generating manifolds of codimension 2 in $\mathbf C^4$. For nonumbilic surfaces we find a class of coordinates which is preserved only by linear transformations. 
@article{IM2_1991_36_3_a8,
     author = {A. V. Loboda},
     title = {Linearizability of holomorphic mappings of generating manifolds of codimension~2 in $\mathbf C^4$},
     journal = {Izvestiya. Mathematics },
     pages = {655--667},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a8/}
}
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A. V. Loboda. Linearizability of holomorphic mappings of generating manifolds of codimension~2 in $\mathbf C^4$. Izvestiya. Mathematics , Tome 36 (1991) no. 3, pp. 655-667. http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a8/