Minimal Legendrian surfaces in the tangent sphere bundle of ℝ3.

In this paper, we study minimal Legendrian surfaces Σ immersed in the tangent sphere bundle T₁ℝ³. 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. [ABSTRACT FROM AUTHOR]