In terms of the quasiperiodically driven Henon map we show that two—dimensional stable invariant manifolds of the nodal invariant curve of а smooth invertible three—dimensional map can possess both differentiable and fractal structure. The fractalization of manifolds precedes the destruction of a smooth invariant curve and the birth of а strange nonchaotic attractor in modeling system. An observation of the angle between manifolds along trajectories that belong to the invariant curve after its manifolds fractalization and the strange nonchaotic attractor shows ап existence оf tangencies of the stable manifolds corresponding to different characteristic exponents. This fact means the violation of parabolic structure of manifolds in a small vicinity of the nodal invariant curve.