First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds

We calculate the first and second variation formulae for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that move the singular set of a C^2 surface and non-singular variations for C^2_h surfaces. These formulae enable us to construct a stability operator for non-singular C^2 surfaces and another one for C^2 (eventually singular) surfaces. Then we can obtain a necessary condition for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in terms of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we give a classification of the complete stable surfaces in the roto-translation group RT.