  The Eisenhart problem of finding parallel tensors treated already in the
framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered
for the symmetric case and the result is interpreted in terms of Ricci
solitons. If the generator of the manifold provides a Ricci soliton then this
is i) expanding on para-Sasakian spaces with constant scalar curvature and
vanishing $D$-concircular tensor field and ii) shrinking on a class of
orientable quasi-umbilical hypersurfaces of a real projective space=elliptic
space form.
