  We prove that, among all (n + 1)-dimensional spin static vacua with positive
cosmological constant, the de Sitter spacetime is characterized by the fact
that its spatial Killing hori-zons have minimal modes for the Dirac operator.
As a consequence, the de Sitter spacetime is the only vacuum of this type for
which the induced metric tensor on some of its Killing horizons is at least
equal to that of a round (n -- 1)-sphere. This extends unique-ness theorems
shown by Boucher-Gibbons-Horowitz and Chruciel to more general horizon metrics
and to the non-single horizon case.
