A Congruence Theorem for Minimal Surfaces in $S^{5}$ with Constant   Contact Angle
  We provide a congruence theorem for minimal surfaces in $S^5$ with constant contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove that Gauss-Codazzi-Ricci equations for minimal surfaces in $S^5$ with constant contact angle satisfy an equation for the Laplacian of the holomorphic angle. Also, we will give a characterization of flat minimal surfaces in $S^5$ with constant contact angle. 
Rodrigo Ristow Montes, Jose A. Verderesi