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Holomorphons and the standard almost complex structure on S^6

Milewski J.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 2

245-254

We consider Euler–Lagrange equations of families of nonnegative functionals defined on tensor fields of the type (1, 1), which are equal to zero only for complex structures tensor fields. As a solution of the equations we define the notion of holomorphon to distinguish a new class of tensor fields on Riemannian manifolds. Next, as our main result, we construct a holomorphon on the 6–dimensional sphere S^6.