WEAKLY EINSTEIN ALMOST COSYMPLECTIC 3-MANIFOLDS

WEAKLY EINSTEIN ALMOST COSYMPLECTIC 3-MANIFOLDS

In this paper, the first thing we prove is that a weakly Einstein cosymplectic 3-manifold is flat and Einstein. Next, we prove that a strictly almost cosymplectic 3-manifold M is weakly Einstein if and only if M has the Ricci tensor of rank one. In particular, if M is strictly H-almost cosymplectic 3-manifolds, then it is locally isomorphic to the Minkowski motion group E₁,₁ equipped with a left invariant almost cosymplectic structure with a² = b². Moreover, we find that there does not exist a weakly Einstein strictly almost cosymplectic 3-manifold with ∇ξh = -2αhφ, for any non-zero constant α.