Sectional curvature rigidity of asymptotically locally hyperbolic manifolds (Q1876577)

Following Witten's proof of the positive mass theorem, Min-Oo showed that any asymptotically hyperbolic spin \(n\)-manifold with scalar curvature \(\geq -n(n-1)\) is isometric to the (real) hyperbolic space. Andersson-Dahl generalized this result to some asymptotically locally hyperbolic (AHL) spin manifolds. The paper under review shows that the ``spin'' assumption can be dropped, provided the sectional curvature is \(\geq -1\). The sectional curvature bound is used to obtain eigenvalue estimates of the curvature endomorphism in the Bochner-Weitzenböck formula.