The identity map as a harmonic map of a \((4r+3)\)-sphere with deformed metrics (Q1316508)
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scientific article; zbMATH DE number 515589
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The identity map as a harmonic map of a \((4r+3)\)-sphere with deformed metrics |
scientific article; zbMATH DE number 515589 |
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The identity map as a harmonic map of a \((4r+3)\)-sphere with deformed metrics (English)
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16 March 1995
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The author studies the instability of the sphere \(S^{4n + 3}\) with metrics \(g(t)\) obtained by specific deformation relative to the Hopf \(S^ 3\)-fibration of \(S^{4n + 3}\). Here instability means that the energy of the identity map has second variation with negative eigenvalues. The corresponding problem relative to the Hopf \(S^ 1\)- fibration of \(S^{2n + 1}\) was treated in [\textit{S. Tanno}, Kodai Math. J. 10, 250-257 (1987; Zbl 0629.53043)].
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identity map
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harmonic instability
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Hopf fibration
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