Minimal Legendrian surfaces in the tangent sphere bundle of R^(3)

In this paper,we study minimal Legendrian surfacesΣimmersed in the tangent sphere bundle T_(1)R^(3).We classify(1)totally geodesic Legendrian surfaces,(2)closed minimal Legendrian surfaces of genus smaller than or equal to 1 and complete minimal Legendrian surfaces with the non-negative Gauss curvature,and(3)complete stable minimal Legendrian surfaces.