Generalized space forms

Authors:
Neil N. Katz and Kei Kondo

Journal:
Trans. Amer. Math. Soc. **354** (2002), 2279-2284

MSC (2000):
Primary 53C21; Secondary 53C20

Published electronically:
February 14, 2002

MathSciNet review:
1885652

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Abstract | References | Similar Articles | Additional Information

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

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Additional Information

**Neil N. Katz**

Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Saga University, Honjoh 1, Saga 840-8502, Japan

Email:
katz@ms.saga-u.ac.jp

**Kei Kondo**

Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Saga University, Honjoh 1, Saga 840-8502, Japan

Email:
kondok@ms.saga-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-02-02966-5

Keywords:
Radial curvature,
rigidity

Received by editor(s):
June 12, 2001

Received by editor(s) in revised form:
September 27, 2001

Published electronically:
February 14, 2002

Additional Notes:
The first author was supported by the Japan Society for the Promotion of Science and Monbusho Grant-in-Aid of Research No. 13099720.

Article copyright:
© Copyright 2002
American Mathematical Society