Basic Gravitational Currents and Killing-Yano Forms

Understand

It has been shown that for each Killing-Yano (KY)-form accepted by an $n$-dimensional (pseudo)Riemannian manifold of arbitrary signature, two basic gravitational currents can be defined.

• Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other.
• Some general geometrical facts implied by these conservation laws are also elucidated.
• In particular, the conservation of the one-form currents implies that the scalar curvature of the manifold is a flow invariant for all of its Killing vector fields.