Minimal Reeb vector fields on almost cosymplectic manifolds

Abstract

We show that the Reeb vector field of an almost cosymplectic three-manifold is minimal if and only if it is an eigenvector of the Ricci operator. Then, we show that Reeb vector field ξ of an almost cosymplectic three-manifold M is minimal if and only if M is (κ, μ, ν)-space on an open dense subset. After, using the notion of strongly normal unit vector field introduced in [8], we study the minimality of ξ for an almost cosymplectic (2n + 1)-manifold. Finally, we classify a special class of almost cosymplectic three-manifold whose Reeb vector field is minimal.