Rigidity of cmc surfaces in the Berger sphere

Abstract

The aim of this paper is to present a formula for the Gaussian curvature of an immersed surface in the Berger sphere \({\mathbb{S}_{\kappa,\tau}^3}\) which involves the contact angle \({\beta}\) . This allows us to conclude that, in the case of \({\kappa-4\tau^2 > 0}\) , the connected CMC compact surface M in this Berger sphere with sign-preserving contact angle must be a Hopf torus.