Riemannian manifolds carrying a pair of skew symmetric conformal vector fields.

We deal with a Riemannian manifold M carrying a pair of skew symmetric conformal vector fields ( X, Y). The existence of such a pairing is determined by an exterior differential system in involution (in the sense of Cartan). In this case, M is foliated by 3-dimensional totally geodesic submanifolds. Additional geometric properties are proved. [ABSTRACT FROM AUTHOR]