Exponential wave maps

We generalize wave maps to exponential wave maps. We compute the first and second variations of the exponential energy, and obtain results concerning the stability of exponential wave maps. We prove a theorem which relates wave maps, exponential wave maps, and the conservation law of second-order symmetric tensors. We show that if ff is an exponential wave and a pseudo-weakly conformal map, then ff is homothetic. We finally discuss the applications of exponential wave maps in relativity.