In the present paper, we study hemi-slant submanifolds of a locally product
Riemannian manifold. We prove that the anti-invariant distribution which is
involved in the definition of hemi-slant submanifold is integrable and give
some applications of this result. We get a necessary and sufficient condition
for a proper hemi-slant submanifold to be a hemi-slant product. We also study
this type submanifolds with parallel canonical structures. Moreover, we give
two characterization theorems for the totally umbilical proper hemi-slant
submanifolds. Finally, we obtain a basic inequality involving Ricci curvature
and the squared mean curvature of a hemi-slant submanifold of a certain type
locally product Riemannian manifold
