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 ξ 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 ξ ( ∇ ξ h = 0), then it is H -almost cosymplectic. In particular, an almost cosymplectic 3 -manifold M satisfying ∇ ξ 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 (κ , μ , ν) -spaces. [ABSTRACT FROM AUTHOR]