1 research outputs found
First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds
We calculate the first and the second variation formula for the
sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We
consider general variations that can move the singular set of a C^2 surface and
non-singular variation for C_H^2 surfaces. These formulas enable us to
construct a stability operator for non-singular C^2 surfaces and another one
for C2 (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
term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally
we classify complete stable surfaces in the roto-traslation group RT .Comment: 36 pages. Misprints corrected. Statement of Proposition 9.8 slightly
changed and Remark 9.9 adde