  Given a closed manifold $M$ and a vector bundle $\xi$ of rank $n$ over $M$,
by gluing two copies of the disc bundle of $\xi$, we can obtain a closed
manifold $D(\xi, M)$, the so-called double manifold.
  In this paper, we firstly prove that each sphere bundle $S_r(\xi)$ of radius
$r>0$ is an isoparametric hypersurface in the total space of $\xi$ equipped
with a connection metric, and for $r>0$ small enough, the induced metric of
$S_r(\xi)$ has positive Ricci curvature under the additional assumptions that
$M$ has a metric with positive Ricci curvature and $n\geq3$.
  As an application, if $M$ admits a metric with positive Ricci curvature and
$n\geq2$, then we construct a metric with positive Ricci curvature on $D(\xi,
M)$. Moreover, under the same metric, $D(\xi, M)$ admits a natural
isoparametric foliation.
  For a compact minimal isoparametric hypersurface $Y^{n}$ in $S^{n+1}(1)$,
which separates $S^{n+1}(1)$ into $S^{n+1}_+$ and $S^{n+1}_-$, one can get
double manifolds $D(S^{n+1}_+)$ and $D(S^{n+1}_-)$. Inspired by Tang, Xie and
Yan's work on scalar curvature of such manifolds with isoparametric
foliations(cf. \cite{TXY12}), we study Ricci curvature of them with
isoparametric foliations in the last part.
