Uniqueness theorem for stationary black ring solution of $\sigma$-models   in five dimensions
  We study axisymmetric self-gravitating non-linear $\sigma$-model in five-dimensional spacetime admitting three commutating Killing vector fields. We show that the only asymptotically flat black ring solution with a regular event horizon is the black ring characterized by mass and two angular momenta with constant mapping. 
Marek Rogatko