Generalized Calabi–Markus conjecture for positive sectional curvature

Let $p\ge q>0$ with $p+q\ge3$. Suppose that $M$ is a complete pseudo-Riemannian manifold of signature $(p,q)$ whose sectional curvature has a positive lower bound.

Generalized Calabi–Markus conjecture. The fundamental group $\pi_1(M)$ is finite, and $M$ is noncompact.

This conjecture generalizes the Calabi–Markus theorem from Lorentz geometry to pseudo-Riemannian manifolds of arbitrary signature satisfying the stated inequalities. The source gives no resolution status.