Constant-mean-curvature conjecture for non-minimal biharmonic submanifolds of spheres

Let $M$ be a non-minimal biharmonic submanifold of the unit sphere $S^n(1)$. Constant-mean-curvature conjecture. The mean curvature of $M$ is constant. The claim is a weaker statement related to the classification of non-minimal biharmonic submanifolds in spheres; the supplied text gives no resolution evidence, so its status is left open.