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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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