  Let $(M,g)$ and $(K,\kappa)$ be two Riemannian manifolds of dimensions $m$
and $k ,$ respectively. Let $\omega\in C^2(N),$ $\omega> 0.$
  The warped product $ M\times _\omega K$ is the $ (m+k)$-dimensional product
manifold $M\times K$ furnished with metric $ g+\omega^2 \kappa.$ We prove that
the supercritical problem $$-\Delta _{g+\omega^2 \kappa}u+h u=u^{ {m+2\over
m-2} \pm\varepsilon},\ u>0,\ \hbox{in}\ (M\times _\omega K,g+\omega^2 \kappa)$$
has a solution which concentrate along a $k$-dimensional minimal submanifold
$\Gamma$ of $M\times _\omega N$ as the real parameter $\varepsilon$ goes to
zero, provided the function $h$ and the sectional curvatures along $\Gamma$
satisfy a suitable condition.
