Nonexistence conjecture for proper biharmonic semi-Riemannian submersions in nonpositive curvature

Let $M$ be a $(2n+1)$-dimensional semi-Riemannian space form $M_{1}^{2n+1}(c)$ of index $1$, and let $B$ be a $2n$-dimensional Riemannian manifold. A proper biharmonic semi-Riemannian submersion is a biharmonic semi-Riemannian submersion that is not harmonic. Nonexistence conjecture. If $c\leq 0$, there exist no proper biharmonic semi-Riemannian submersions

$$\pi:M\rightarrow B.$$

This proposes a higher-dimensional analogue of the preceding three-dimensional nonexistence result for proper biharmonic semi-Riemannian submersions in nonpositive curvature. Its resolution is not established by the supplied text.