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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Polar coordinates induced by actions of compact Lie groups


Author: Jiri Dadok
Journal: Trans. Amer. Math. Soc. 288 (1985), 125-137
MSC: Primary 22E15; Secondary 53C35
MathSciNet review: 773051
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Abstract: Let $ G$ be a connected Lie subgroup of the real orthogonal group $ O(n)$. For the action of $ G$ on $ {{\mathbf{R}}^n}$, we construct linear subspaces $ \mathfrak{a}$ that intersect all orbits. We determine for which $ G$ there exists such an $ \mathfrak{a}$ meeting all the $ G$-orbits orthogonally; groups that act transitively on spheres are obvious examples. With few exceptions all possible $ G$ arise as the isotropy subgroups of Riemannian symmetric spaces.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0773051-1
PII: S 0002-9947(1985)0773051-1
Keywords: Orbits, linear cross sections
Article copyright: © Copyright 1985 American Mathematical Society