On certain surfaces in the isotropic 4-space

The isotropic space is a special ambient space obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we establish a method to calculate the second fundamental form of surfaces in the isotropic 4-space. Further, we classify some surfaces (spherical product surfaces and Aminov surfaces) in the isotropic 4-space with vanishing curvatures.