Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Newman's theorem in the Riemannian category


Authors: L. N. Mann and J. L. Sicks
Journal: Trans. Amer. Math. Soc. 210 (1975), 259-266
MSC: Primary 57E10
MathSciNet review: 0423388
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57E10

Retrieve articles in all journals with MSC: 57E10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0423388-4
PII: S 0002-9947(1975)0423388-4
Keywords: Newman's theorem on periodic transformations, groups of isometries, diameter of orbits, radius of convexity
Article copyright: © Copyright 1975 American Mathematical Society