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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reduction of variables for minimal submanifolds


Authors: Richard S. Palais and Chuu-Lian Terng
Journal: Proc. Amer. Math. Soc. 98 (1986), 480-484
MSC: Primary 53C12; Secondary 53C42
MathSciNet review: 857946
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Abstract: If $ G$ is a compact Lie group and $ M$ a Riemannian $ G$ manifold, then the orbit map $ \prod :M \to 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 $ \prod $ which we call $ h$-projectability and which is shared by certain other naturally occurring and important classes of Riemannian submersions.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0857946-2
PII: S 0002-9939(1986)0857946-2
Article copyright: © Copyright 1986 American Mathematical Society