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Uniqueness theorem for stationary black hole solutions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>-models in five dimensions
I prove the uniqueness theorem for stationary self-gravitating nonlinear $\ensuremath{\sigma}$-models in five-dimensional spacetime. I show that the Myers-Perry vacuum Kerr spacetime is the only maximally extended, stationary, axisymmetric asymptotically flat solution having the regular rotating event horizon with a constant mapping.