  The critical point equation arises as a critical point of the total scalar
curvature functional defined on the space of constant scalar curvature metrics
of a unit volume on a compact manifold. In this equation, there exists a
function $f$ on the manifold that satisfies the following
  $$
  (1+f){\rm Ric} = Ddf + \frac{nf +n-1}{n(n-1)}sg.
  $$
  It has been conjectured that if $(g, f)$ is a solution of the critical point
equation, then $g$
  is Einstein and so $(M, g)$ is isometric to a standard sphere.
  In this paper, we show that this conjecture is true if the given Riemannian
metric has positive isotropic curvature.
