Instability of the nearly-Kähler six-sphere. (English) Zbl 0765.53025

Wood, C. M.

J. Reine Angew. Math. 439, 205-212 (1993).

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.

Reviewer: C.M.Wood (Heslington)

MSC:

53C15

General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords:

almost-Hermitian structure; twistor bundle; energy functional; nearly- Kähler structure; six-sphere