The hyperbolic paraboloid is not an isometric embedding of the hyperbolic plane H2 in Euclidean space E3, because it does not have constant negative Gaussian curvature.
In general it is impossible to have an isometric embedding of H2 in E3, although it is possible to have isometric embeddings of fragments of H2.
In general it is impossible to have an isometric embedding of H2 in E3, although it is possible to have isometric embeddings of fragments of H2.