  We study non-linear electrodynamics in curved space from the viewpoint of
dualities. After establishing the existence of a topological bound for
self-dual configurations of Born-Infeld field in curved space, we check that
the energy-momentum tensor vanishes. These properties are shown to hold for
general duality-invariant non-linear electrodynamics. We give the dimensional
reduction of Born-Infeld action to three dimensions in a general curved
background admitting a Killing vector. The SO(2) duality symmetry becomes
manifest but other symmetries present in flat space are broken, as is U-duality
when one couples to gravity. We generalize our arguments on duality to the case
of n U(1) gauge fields, and present a new Lagrangian possessing SO(n) X
SO(2)_elemag duality symmetry. Other properties of this model such as Legendre
duality and enhancement of the symmetry by adding dilaton and axion, are
studied. We extend our arguments to include a background b-field in the curved
space, and give new examples including almost Kaehler manifolds and
Schwarzshild black holes with a $b$-field.
