  We consider the problem for the classification of static and asymptotically
flat Einstein-Maxwell-dilaton spacetimes with a photon sphere. It is first
proven that the photon spheres in Einstein-Maxwell-dilaton gravity have
constant mean and constant scalar curvature. Then we derive some relations
between the mean curvature and the physical characteristics of the photon
spheres. Using further the symmetries of the dimensionally reduced
Einstein-Maxwell-dilaton field equations we show that the lapse function, the
electrostatic potential and the dilaton field are functionally dependent in the
presence of a photon sphere. Using all this we prove the main classification
theorem by explicitly constructing all Einstein-Maxwell-dilaton solutions
possessing a non-extremal photon sphere.
