Weakly η-Einstein Almost Cosymplectic $3$-Manifolds

We show that a strictly almost cosympletic $3$-manifold M is weakly η-Einstein if and only if M is weakly Einstein. On the other hand, a cosympletic $3$-manifold M is weakly η-Einstein if and only if M is η-Einstein. If the scalar curvature r of a cosymplectic $3$-manifold M is zero, then M is Einstein, weakly Einstein, and flat.