Remarks on Almost Cosymplectic 3-Manifolds with RICCI Operators

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.

Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.