Geodesic
On algebraic-geometry methods for constructing submanifolds with flat normal bundle and holonomic net of curvature lines
Funkcionalʹnyj analiz i ego priloženiâ, Tome 54 (2020) no. 3, pp. 26-37

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In this paper we propose a generalization of Krichever's algebraic-geometric construction of orthogonal coordinate systems in a flat space. In the theory of integrable systems of hydrodynamic type a fundamental role is also played by orthogonal coordinates in some special nonflat spaces. The most important class of such spaces is given by metrics of submanifolds in flat spaces that have flat normal bundle and holonomic net of curvature lines, which defines orthogonal coordinates on the submanifold. We propose a method for constructing such submanifolds from algebraic-geometric data. Explicit examples are presented.
Keywords: submanifold with flat normal bundle, orthogonal coordinates, algebraic-geometric data, holonomic net of curvature lines, diagonal metric with diagonal curvature. 
@article{FAA_2020_54_3_a2,
     author = {E. V. Glukhov and O. I. Mokhov},
     title = {On algebraic-geometry methods for constructing submanifolds with flat normal bundle and holonomic net of curvature lines},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {26--37},
     publisher = {mathdoc},
     volume = {54},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2020_54_3_a2/}
}
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E. V. Glukhov; O. I. Mokhov. On algebraic-geometry methods for constructing submanifolds with flat normal bundle and holonomic net of curvature lines. Funkcionalʹnyj analiz i ego priloženiâ, Tome 54 (2020) no. 3, pp. 26-37. http://geodesic.mathdoc.fr/item/FAA_2020_54_3_a2/