Di Scala's conjecture on minimal immersions into nonpositively curved space forms

Let $M^n$ be a Riemannian manifold that is either locally homogeneous or Einstein. Let

$$f:M^n\rightarrow \mathbb{Q}_c^{n+p}$$

be a minimal isometric immersion, where $c\leq 0$.

Di Scala's conjecture. The immersion $f$ must be totally geodesic.

The conjecture extends the known result that the only minimal extrinsically homogeneous submanifolds of hyperbolic space are totally geodesic. Its status is not determined by the supplied text.