Obstructions to positive curvature and symmetry

الأصل · EN

We show that the indices of certain twisted Dirac operators vanish on a Spin-manifold M of positive sectional curvature if the symmetry rank of M is ≥ 2 or if the symmetry rank is one and M is two connected. We also give examples of simply connected manifolds of positive Ricci curvature which do not admit a metric of positive sectional curvature and positive symmetry rank.