Torus actions and positive and non-negative curvature
- We investigate questions concerning symmetries and Riemannian metrics of positive or non-negative curvature. To be more precise, we discuss the question if a non-trivial circle action on a manifold implies the existence of an (invariant) metric of positive scalar curvature. Moreover, we classify those simply-connected torus manifolds which admit an invariant metric of non-negative sectional curvature. First results concerning the homotopy type of the moduli space of invariant metrics of positive scalar curvature on a quasitoric manifold are also presented.
Here a torus manifold is an even-dimensional manifold with an effective action of a half-dimensional torus which has fixed points. Quasitoric manifolds are special torus manifolds with an orbit space diffeomorphic to a simple convex polytope.