To get started, a Legendrian vector field can be defined by considering a surface Σ in a 3-dimensional pseudo-hermitian manifold. Then, JIH-HSIN CHENG and 3 others observe that to every non-singular point of Σ, we associate a vector field normal to Σ. For more about this, see
MINIMAL SURFACES IN PSEUDOHERMITIAN GEOMETRY AND THE BERNSTEIN PROBLEM IN THE HEISENBERG GROUP