On the cosymplectic conformal curvature tensor (Q2782770)

The cosymplectic conformal curvature tensor on a cosymplectic manifold is computed in local coordinates. Some consequences are derived: (i) if the cosymplectic conformal curvature tensor of a cosymplectic manifold \(M\) vanishes then the conformal curvature tensor of a transversal Kählerian hypersurface of \(M\) vanishes; (ii) the Ricci contraction of the cosymplectic conformal curvature tensor of a cosymplectic manifold \(M\) of dimension \(>5\) vanishes if and only if \(M\) is \(\eta \)-Einstein; (iii) the Ricci contraction of the cosymplectic conformal tensor of a cosymplectic manifold of dimension \(>5\) is parallel if and only if the Ricci tensor is parallel.