## Generalized space forms.(English)Zbl 0990.53032

Summary: Spaces with radially symmetric curvature at base point $$p$$ are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to $${\mathbb R^n}$$ or $$S^n$$ under a radially symmetric metric, to $${\mathbb R}\text{P}^n$$ 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 $$p$$.

### MSC:

 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C20 Global Riemannian geometry, including pinching