the first order ASDYM equations (\[2.7\]) to higher dimensions [@CDFN]-[@Tian] with some explicit solutions (see e.g. [@FN]). In particular, in $d{=}2n{=}6$ one can consider the equations [@Tian] $$\label{2.8}
*{{\cal F}}=-\o\wedge{{\cal F}}\ ,$$ where $\o$ is a two-form. Differentiating (\[2.8\]), we obtain $$\label{2.9}
\diff (*{{\cal F}})+{{\cal A}}\wedge*{{\cal F}}-*{{\cal F}}\wedge{{\cal A}}+*H\wedge{{\cal F}}=0\ ,$$ where the 3-form $H$ is defined by the formula $$\label{2.10}
H:=*\diff\o\ .$$ Equations (\[2.9\]) differ from the standard Yang-Mills equations by the last term with a 3-form $H$ which can be identified with a totally antisymmetric torsion. These equations naturally appear in string theory.

For manifolds $X^6$ with an almost complex structure ${{\cal J}}$ the equations (\[2.8\]) can be rewritten in the form (\[2.6\]) with an almost Hermitian structure $\o$. To each solution ${{\cal A}}$ of the HYM equation (\[2.6\]) there corresponds a pseudo-holomorphic structure on the vector bundle ${{\cal E}}$ over $X^6$. In the case of integrable almost complex structure ${{\cal J}}$ the first equation in (\[2.6\]) defines a holomorphic structure on ${{\cal E}}$ and the second equation in (\[2.6\]) is the requirement of (semi)stability of the bundle ${{\cal E}}$ [@Don; @UY]. Thus, for complex manifolds the HYM connections ${{\cal A}}$ (solutions to (\[2.6\])) describe (semi)stable holomorphic bundles 