Reduction of Variables for Minimal Submanifolds

If G is a compact Lie group and M a Riemannian G manifold, then the orbit map Π: M → M/G is a stratified Riemannian submersion and the well-known "cohomogeneity method" pioneered by Hsiang and Lawson [HL] reduces the problem of finding codimension k minimal submanifolds of M to a related p...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1986, Vol.98 (3), p.480-484
Main Authors: Palais, Richard S., Terng, Chuu-Lian
Format: Article
Language:English
Subjects:
Critical points
Curvature
Exact sciences and technology
Geometry, differential geometry, and topology
Lie groups
Mathematical independent variables
Mathematical methods in physics
Mathematical variables
Physics
Riemann manifold
Vector fields
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Summary:If G is a compact Lie group and M a Riemannian G manifold, then the orbit map Π: M → M/G is a stratified Riemannian submersion and the well-known "cohomogeneity method" pioneered by Hsiang and Lawson [HL] reduces the problem of finding codimension k minimal submanifolds of M to a related problem in M/G. We show that this reduction of variables technique depends only on a certain natural Riemannian geometric property of the map Π which we call h-projectability and which is shared by certain other naturally occurring and important classes of Riemannian submersions.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1986-0857946-2