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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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Polar coordinates induced by actions of compact Lie groups
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by Jiri Dadok PDF
Trans. Amer. Math. Soc. 288 (1985), 125-137 Request permission

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
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 288 (1985), 125-137
  • MSC: Primary 22E15; Secondary 53C35
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0773051-1
  • MathSciNet review: 773051