A sphere theorem for radial curvature (Q2444972)

The authors examine the radial curvature and the topology of a pointed compact Riemannian manifold \((M,g)\) of dimension \(m\) and establish a new topological sphere theorem assuming that the reference surfaces are compact surfaces of revolution. A Alexandrov-Toponogov comparison theorem [the authors, ibid. 24, No. 2, 57--91 (2013; Zbl 1296.53067)] plays a central role.