## 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 $p$.## References

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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
- MR Author ID: 690980
- 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
- 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.
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 2279-2284 - MSC (2000): Primary 53C21; Secondary 53C20
- DOI: https://doi.org/10.1090/S0002-9947-02-02966-5
- MathSciNet review: 1885652