  In this paper, we study translation surfaces in the Euclidean space endowed
with a canonical semi-symmetric non-metric connection. We completely classify
the translation surfaces of constant sectional curvature with respect to this
connection, proving that they are generalized cylinders. This consequence is
the same as in the case of the Levi-Civita connection, but in this new setting,
there are also generalized cylinders whose sectional curvature can be constant
or non-constant, in contrast to the Levi-Civita connection, where the Gaussian
curvature is zero.
