Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E15, 53C35

Retrieve articles in all journals with MSC: 22E15, 53C35

Additional Information

Keywords: Orbits, linear cross sections
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society