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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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Newman’s theorem in the Riemannian category
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by L. N. Mann and J. L. Sicks PDF
Trans. Amer. Math. Soc. 210 (1975), 259-266 Request permission

Abstract:

In 1931 M. H. A. Newman proved that if $M$ is a connected topological manifold with metric $d$, there exists a number $\varepsilon > 0$, depending only upon $M$ and $d$, such that every compact Lie group $G$ acting effectively on $M$ has at least one orbit of diameter at least $\varepsilon$. Aside from isolated results nothing appears to be known about $\varepsilon$. In order to learn more about the invariant $\varepsilon$, attention is restricted here to groups of isometries on a Riemannian manifold. It is found that the invariant $\varepsilon$ of $M$ is connected with the notion of convexity introduced by J. H. C. Whitehead in 1932.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 210 (1975), 259-266
  • MSC: Primary 57E10
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0423388-4
  • MathSciNet review: 0423388