Is it possible/correct to describe electromagnetism using curved space(-time)? Comparing the simples form of the forces of both phenomena: the law of Newton for gravitation  $V\propto \frac{1}{r}$, and the Coulomb law for electrostatics $V\propto \frac{1}{r}$, one might think that if one can be extended relativistically to a curvature in space-time, that the other one would lend itself to a similar description. Is this so?
Thanks for any useful thoughts and/or suggestions!
 A: I don't really follow the text underneath the title, but the answer to this
question is most certainly, yes.  (For example, we witness electromagnetic
waves traveling through curved space.)  Here is how electromagnetism is
described mathematically (I fear this answer is slightly beyond the level of the
questioner -- sorry -- but perhaps not of other readers):
Maxwell's equations are best expressed in terms of the field strength
tensor.  That tensor is the curvature of a connection on a circle bundle
(over spacetime).  The connection is the four-vector electromagnetic
potential, in physics terms.  In this set up, two of Maxwell's equations
are automatic (for example, saying that the magnetic field is locally the curl
of a 3-vector is saying that it is divergence-free).  The other two are
equations for the "divergence" of this tensor.  This way of phrasing
the problem makes sense in any metric, i.e. on curved spacetimes.
A: Everyone else here is right, but there is also an unmentioned complication to using curvature to explain electromagnetic forces:
We use curvature to explain gravity in an attempt to explain why intertial and gravitational masses are the same--why a bowling ball falls the same rate as a penny.  Einstein's answer was that it's because they're just travelling in 'straight' lines in the same spacetime, and aren't feeling any forces at all--they're just trying to move in the straightest line they can.  
But with E&M, not all charges feel the same force in a given electric field--in fact, chargless particles feel no force at all!  So, if we're going to explain E&M using curvature, we're going to need to explain why different particles have different charges.  
A: I'm not sure if this is exactly what you're getting at, but there have been attempts to derive electromagnetism as a consequence of general relativity. The most famous one is Kaluza-Klein theory, published in 1921. The theory is basically just general relativity in a 5-dimensional spacetime, where one of the dimensions is "curled up" (compact). It turns out that the additional equations of motion obtained from the compact dimension are equivalent to the Maxwell equations for electromagnetism (in the relativistic form Eric described).
