  The coupling of conserved p-brane currents with non-Abelian gaugetheories is
done consistently by using Chern-Simons forms. Conserved currents localized on
p-branes that have a gravitational origin can be constructed from Killing-Yano
forms of the underlying spacetime. We propose a generalization of the coupling
procedure with Chern-Simons gravities to the case of gravitational conserved
currents. In odd dimensions, the field equations of coupled Chern-Simons
gravities that describe the local curvature on p-branes are obtained. In
special cases of three and five dimensions, the field equations are
investigated in detail.
