Minimal isometric immersion conjecture for locally homogeneous or Einstein manifolds

Let $M$ be a Riemannian manifold that is either locally homogeneous or Einstein, and let $f:M\rightarrow\mathbb{R}^n$ be a minimal isometric immersion.

Minimal immersion conjecture. The immersion $f$ must be totally geodesic.

This conjecture concerns the rigidity of minimal isometric immersions and was posed in the context of minimal homogeneous submanifolds. The supplied source does not indicate whether it has been resolved.