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Mathematische Annalen

, Volume 341, Issue 4, pp 845–858 | Cite as

Smooth circle actions on highly symmetric manifolds

  • Krzysztof Pawałowski
Article

Abstract

We construct for the first time smooth circle actions on highly symmetric manifolds such as disks, spheres, and Euclidean spaces which contain two points with the same isotropy subgroup whose representations determined on the tangent spaces at the two points are not isomorphic to each other. This allows us to answer negatively a question of Hsiang and Hsiang [Some Problems in Differentiable Transformation Groups, Springer, Berlin, Problem 16, p. 228, 1968].

Mathematical Subject Classification (2000).

57S15 57S25 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznanPoland

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