Pseudo-symmetric almost cosymplectic 3-manifolds

Abstract

In this paper, we study the semi-symmetry and pseudo-symmetry of almost cosymplectic [Formula: see text]-manifolds. First, we prove that an [Formula: see text]-almost cosymplectic [Formula: see text]-manifold [Formula: see text] is semi-symmetric if and only if it is cosymplectic. Here by an [Formula: see text]-almost cosymplectic [Formula: see text]-manifold, we mean an almost cosymplectic [Formula: see text]-manifold whose characteristic vector field [Formula: see text] is a harmonic unit vector field. If an almost cosymplectic [Formula: see text]-manifold [Formula: see text] whose fundamental endomorphism field [Formula: see text] is parallel in the direction of the characteristic vector field [Formula: see text] ([Formula: see text]), then it is [Formula: see text]-almost cosymplectic. In particular, an almost cosymplectic [Formula: see text]-manifold [Formula: see text] satisfying [Formula: see text] is semi-symmetric if and only if it is cosymplectic. Next, we prove that pseudo-symmetric [Formula: see text]-almost cosymplectic [Formula: see text]-manifolds are certain generalized almost cosymplectic [Formula: see text]-spaces.