Reduction of variables for minimal submanifolds
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- by Richard S. Palais and Chuu-Lian Terng PDF
- Proc. Amer. Math. Soc. 98 (1986), 480-484 Request permission
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.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 480-484
- MSC: Primary 53C12; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-1986-0857946-2
- MathSciNet review: 857946