ON APPROXIMATELY INTEGRABLE SO(3) STRUCTURES ON 5-DIMENSIONAL MANIFOLDS

In this work, irreducible SO(3) structures on a 5-dimentional manifold are considered. The covariant divergence of the structure tensor is shown to be zero for approximately integrable irreducible SO(3) structures. Examples of left invariant irreducible SO(3) structures on 5-dimentional Lie groups that have a zero covariant divergence of the structure tensor but are not approximately integrable, as well as of irreducible SO(3) structures with nonzero covariant divergence of the structure tensor are presented.