Singular Minimal Surfaces which are Minimal

In the present paper, we discuss singular minimal surfaces in Euclidean $3-$space $\mathbb{R}^{3}$ which are minimal. Such a surface is nothing but plane, trivial outcome. However, non-trivial outcome obtained when modify usual condition of minimality by using special semi-symmetric metric connection instead Levi-Civita on $\mathbb{R}^{3}$. With this new connection, prove that, besides planes, generalized cylinders, providing their explicit equations. A observed use non-metric connection. Furthermore, our discussion adapted to Lorentz-Minkowski 3-space.