The identity map as a harmonic map of a \((4r+3)\)-sphere with deformed metrics
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)].
scientific article; zbMATH DE number 515589