We study non-linear electrodynamics in curved space from the viewpoint of<br />
dualities. After establishing the existence of a topological bound for<br />
self-dual configurations of Born-Infeld field in curved space, we check that<br />
the energy-momentum tensor vanishes. These properties are shown to hold for<br />
general duality-invariant non-linear electrodynamics. We give the dimensional<br />
reduction of Born-Infeld action to three dimensions in a general curved<br />
background admitting a Killing vector. The SO(2) duality symmetry becomes<br />
manifest but other symmetries present in flat space are broken, as is U-dua...