For solving Navier-Stokes equationsformulawhere ~V (~x; t) is the fluid velocity, P(~x; t) is the pressure and ¹ is the viscosity of liquid, are used the conditions of their compatibility in the form of conservation laws formulaThe 6D-space with the metric   formula  the metric (2) is simplified and solutions of the NS-equations are expressed in terms of the function P(x) that satisfies the Monge-Ampere equation. A more general approach to obtain the solutions of the NS-equations is connected by using the 14D space with condition on the Ricci curvature Rik = 0 on solutions of the NS system. Theorem. The metricsformulais applied to construct an example of solutions of the NS-equations.In particular caseformulais the Ricci-flat on solutions of the equations (1). The Cartan Invariants K = R(a; j; b;i )R(c; i; d;j )AaAbAcAd of the metrics are used to construct solutions of the equations NS and their properties are discussed.