ИСТИНА

An algebro–geometric approach to submanifolds with flat normal bundle is presented. The construction introduced in the work is a generalization of Krichever construction for orthogonal coordinate systems in flat spaces. We develop Krichever ideas and obtain formulae for embedding functions for the submanifold in terms of theta–functions of a complex curve. We also discuss some geometrical properties of the constructed submanifolds. Following the ideas of Ferapontov we describe an integrable class of hydrodynamic type system in terms of the metric and the Weingarten map of the submanifold.