Torus actions on manifolds of positive sectional curvature.
The author proves several new theorems on isometric torus actions on Riemannian manifolds of positive sectional curvature. While these theorems are too complicated to present in the brief space of a review, they represent a significant contribution to the literature. Contents include: an introduction (containing a broad overview of the topic); proof of the connectedness lemma; upper bounds on error-correcting codes; a recognition theorem for the sphere; cyclic group actions with connected fixed-point sets; totally geodesic submanifolds; proof of theorem 2--5; proof of theorem 4; proof of theorem 3; and a bibliography of twenty-seven items.
Riemannian manifolds of positive sectional curvature
scientific article; zbMATH DE number 2115789
scientific article