Weierstrass Representation for Minimal Surfaces into BCV-Spaces

Bianchi-Cartan-Vranceanu spaces (BCV-spaces) are some 3-dimensional homogeneous manifolds equiped with a metric depending on 2 parameters $\kappa$ and $\tau$, and whose isometries groups are of dimension four. In this paper, we describe a Weierstrass-type representation formula for simply connected minimal surfaces immersed into BCV-spaces.