Abstract
Let M be an almost cosymplectic 3-h-a-manifold. In this paper, we prove that the Ricci operator of M is transversely Killing if and only if M is locally isometric to a product space of an open interval and a surface of constant Gauss curvature, or a unimodular Lie group equipped with a left invariant almost cosymplectic structure. Some corollaries of this result and some examples illustrating main results are given.
Highlights
An almost cosymplectic manifold can be regarded as an odddimensional analogy of almost Kahler manifolds from topological points of view and was first introduced by Goldberg and Yano in [2]
E curvature properties of cosymplectic manifolds were first studied by Blair who in [11] proved that a cosymplectic manifold of constant sectional curvature is locally flat
Cho, in [15], studied Reeb flow symmetry on almost cosymplectic 3-manifolds
Summary
An almost cosymplectic manifold can be regarded as an odddimensional analogy of almost Kahler manifolds from topological points of view (see [1]) and was first introduced by Goldberg and Yano in [2]. In [20], Blair applied (1) for the structure tensor field to give a characterization for an almost contact metric manifold to be cosymplectic.
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