Holomorphons and the standard almost complex structure on $S^6$

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 $S^6$.