A General Theory of Canonical Forms

Richard S. Palais, Chuu-Lian Terng

Type: Article

Publication Date: 1987-04-01

Citations: 33

DOI: https://doi.org/10.2307/2000369

Abstract

If $G$ is a compact Lie group and $M$ a Riemannian $G$-manifold with principal orbits of codimension $k$ then a section or canonical form for $M$ is a closed, smooth $k$-dimensional submanifold of $M$ which meets all orbits of $M$ orthogonally. We discuss some of the remarkable properties of $G$-manifolds that admit sections, develop methods for constructing sections, and consider several applications.

Locations

Transactions of the American Mathematical Society - View - PDF

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