  Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical
semi-symmetric non-metric connection determined by a vector field
$\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional
curvature with respect to this connection is constant. In case that the surface
is cylindrical, we obtain full classification when the rulings are orthogonal
or parallel to $\mathsf{C}$. If the surface is rotational, we prove that the
rotation axis is parallel to $\mathsf{C}$ and we classify all conical
rotational surfaces with constant sectional curvature. Finally, for the
particular case $\frac12$ of the sectional curvature, the existence of
rotational surfaces orthogonally intersecting the rotation axis is also
obtained.
