Pseudo-symmetric almost cosymplectic 3-manifolds

In this paper, we study the semi-symmetry and pseudo-symmetry of almost cosymplectic 3-manifolds. First, we prove that an H-almost cosymplectic 3-manifold M is semi-symmetric if and only if it is cosymplectic. Here by an H-almost cosymplectic 3-manifold, we mean an almost cosymplectic 3-manifold whose characteristic vector field xi is a harmonic unit vector field. If an almost cosymplectic 3-manifold M whose fundamental endomorphism field h is parallel in the direction of the characteristic vector field xi (del(xi)h = 0), then it is H-almost cosymplectic. In particular, an almost cosymplectic 3-manifold M satisfying del(xi)h = 0 is semi-symmetric if and only if it is cosymplectic. Next, we prove that pseudo-symmetric H-almost cosymplectic 3-manifolds are certain generalized almost cosymplectic (kappa, mu, v)-spaces.