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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-02-02966-5
Published electronically: February 14, 2002
MathSciNet review: 1885652
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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 ${\mathbb R}{\rm P}^n$ 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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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

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