Isometric immersions of two-dimensional Riemannian metrics of negative curvature into \(E^3\) (Q1358349)

The paper considers isometric immersions of two-dimensional metrics of negative curvature into Euclidean 3-space \(E^3\). The impossibility of some special configuration of asymptotic lines on a Lobachevskij plane region immersed into \(E^3\) is proved. Equations of virtual asymptotic nets on manifolds of negative curvature are studied, and it is proved that if the characteristics of different families of these equations are tangent at a point, then they coincide and form a geodesic line.