Minimal Legendrian surfaces in the tangent sphere bundle of {\mathbb{S}}^3.

In this paper we study minimal Legendrian surfaces \Sigma immersed in tangent sphere bundle T_1{\mathbb {S}}^3. We classify (1) totally geodesic Legendrian surfaces, (2) closed minimal Legendrian surfaces of genus smaller than or equal to one and complete minimal Legendrian surfaces with non-negative Gauss curvature. [ABSTRACT FROM AUTHOR]