Resumen de On the geometry of spheres with positive curvature
Let M be an n-dimensional complete connected Riemannian manifold with sectional curvature bigger than or equal to 1 and diameter bigger than p/2, and N be a closed connected totally geodesic submanifold. In this paper we show that N is homeomorphic to a sphere if there exist a point x in N with rad(x) in M bigger than p/2. If we further assume that the radius of M is bigger than p/2, we give a two-dimensional example to show that the antipodal map A of M restricted to a complete totally geodesic submanifold may not agree with that of M.
