Contact angle for immersed surfaces in S2n+1

In this paper we introduce the notions of contact angle and of holomorphic angle for immersed surfaces in odd dimensional spheres. We deduce formulas for the Laplacian and for the Gaussian curvature, and we classify minimal surfaces in S5 with the two angles constant. This classification gives a 2-parameter family of minimal tori of S5. Also, we give an alternative proof of the classification of minimal Legendrian surfaces of S5 with constant Gaussian curvature.