  In this paper, we study the Einstein multiply warped products with a
semi-symmetric non-metric connection and the multiply warped products with a
semi-symmetric non-metric connection with constant scalar curvature, we apply
our results to generalized Robertson-Walker spacetimes with a semi-symmetric
non-metric connection and generalized Kasner spacetimes with a semi-symmetric
non-metric connection and find some new examples of Einstein affine manifolds
and affine manifolds with constant scalar curvature.{\ss} We also consider the
multiply warped products with an affine connection with a zero torsion.
