  Rigidity results for asymptotically locally hyperbolic manifolds with lower
bounds on scalar curvature are proved using spinor methods related to the
Witten proof of the positive mass theorem. The argument is based on a study of
the Dirac operator defined with respect to the Killing connection. The
existence of asymptotic Killing spinors is related to the spin structure on the
end. The expression for the mass is calculated and proven to vanish for
conformally compact Einstein manifolds with conformal boundary a spherical
space form, giving rigidity. In the 4-dimensional case, the signature of the
manifold is related to the spin structure on the end and explicit formulas for
the relevant invariants are given.
