Uniqueness Theorem for Static Black Hole Solutions of sigma-models in   Higher Dimensions
  We prove the uniqueness theorem for self-gravitating non-linear sigma-models in higher dimensional spacetime. Applying the positive mass theorem we show that Schwarzschild-Tagherlini spacetime is the only maximally extended, static asymptotically flat solution with non-rotating regular event horizon with a constant mapping. 
Marek Rogatko