Generalized space forms

Spaces with radially symmetric curvature at base point p are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to R-n or S-n under a radially symmetric metric, to RPn with Riemannian universal covering of S-n equipped with a radially symmetric metric, or else have constant curvature outside a metric ball of radius equal to the injectivity radius at p.