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Stability of natural energy functionals at Riemannian subimmersions. (English) Zbl 1085.58011

For \(\Phi\) a function on the symmetric matrices which is invariant under conjugation by orthogonal matrices, the \(\Phi\)-energy of a smooth mapping between Riemannian manifolds is (well-)defined to be \(E_{\Phi}(f):=\int\Phi(df^*df)\). The most prominent examples are the energy \(\int| df| ^2\), the volume, and the Jacobians.
For the \(\Phi\)-energies, the first and second variation are computed. This results in some stability criteria for these energies at Riemannian subimmersions.

MSC:

58E20 Harmonic maps, etc.
53C43 Differential geometric aspects of harmonic maps
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References:

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