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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.

Some geometric structures on the tangent bundle of a Riemannian manifold

Papaghiuc N.

Demonstratio Mathematica

2004

Vol. 37, nr 1

215--228

It is defined a new almost complex structure with Norden metric (hyperbolic metric) on the tangent bundle TM of an n- dimensional Riemannian manifold M. Next, the conditions under which the considered almost complex structure with Norden metric belongs to one of the eight classes of almost complex manifolds with Norden metric obtained by G. T. Ganchev and D. V. Borisov in the classification from [2] there are studied.