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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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Characterizations of simply connected rotationally symmetric manifolds
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by Hyeong In Choi PDF
Trans. Amer. Math. Soc. 275 (1983), 723-727 Request permission

Abstract:

We prove that a simply connected, complete Riemannian manifold $M$ is rotationally symmetric at $p$ if and only if the exponential image of every linear subspace of ${M_p}$ is a smooth, closed, totally geodesic submanifold of $M$. This result is in essence Schur’s theorem at one point $p$, as it becomes apparent in the proof.
References
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 275 (1983), 723-727
  • MSC: Primary 53C21; Secondary 53C25
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0682727-4
  • MathSciNet review: 682727