Generalized space forms

Katz, Neil; Kondo, Kei

doi:10.1090/S0002-9947-02-02966-5

Generalized space forms
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by Neil N. Katz and Kei Kondo PDF

Trans. Amer. Math. Soc. 354 (2002), 2279-2284 Request permission

Abstract:

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 ${\mathbb R}\textrm {P}^n$ 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 $p$.

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