Classical Kalb-Ramond field theory in curved spacetimes

We propose to develop the Kalb-Ramond theory in four-dimensional spacetime at level of a classical field by following same formal development steps as Maxwell standard electrodynamics. Solutions presence static sources various curved spacetimes are then analyzed. A question that we address here is possible polarization spacetimes, like one can encounter dielectric ordinary electrodynamics certain types spacetimes.