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Instability of the nearly-Kähler six-sphere. (English) Zbl 0765.53025
An almost-Hermitian structure is said to be harmonic if the parametrizing section of the twistor bundle is a critical point of the energy functional, with respect to variations through sections. It is shown that every nearly-Kähler structure is harmonic, in particular the standard almost-complex structure on the six-sphere. However, the latter is unstable, there being a 7-parameter family of energy-decreasing variations through nearby almost-Hermitian structures.

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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