Local differential-geometric properties of three-webs ##IMG## [http://ej.iop.org/images/1064-5616/211/6/875/toc_MSB_211_6_875ieqn1.gif] {$W(r, r, 2)$} formed on a ##IMG## [http://ej.iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn2.gif] {$2r$} -dimensional manifold by foliations of codimension ##IMG## [http://ej.iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn3.gif] {$r$} , ##IMG## [http://ej.iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn3.gif] {$r$} and ##IMG## [http://ej.iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn4.gif] {$2$} , respectively, are considered. In particular, three-webs defined by complex analytic functions of ##IMG## [http://ej.iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn3.gif] {$r$} complex arguments belong to this class of webs. The structure equations of a three-web ##IMG## {$W(r, r, 2)$...}

中文翻译：

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三网## IMG ## [http://ej.iop.org/images/1064-5616/211/6/875/toc_MSB_211_6_875ieqn1.gif] {$ W（r，r，2）$}

三网## IMG ## [http://ej.iop.org/images/1064-5616/211/6/875/toc_MSB_211_6_875ieqn1.gif] {$ W（r，r，2 ）$}在## IMG ##上形成[http://ej.iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn2.gif] {$ 2r $}-维流形，由余量维数## IMG ## [http://ej.iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn3.gif] {$ r $}，## IMG ## [http：// ej。 iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn3.gif] {$ r $}和## IMG ## [http://ej.iop.org/images/1064-5616/211/分别考虑6/875 / MSB_211_6_875ieqn4.gif] {$ 2 $}。特别是，由## IMG ## [http://ej.iop.org/images/1064-5616/211/6/875/MSB_211_6_875ieqn3.gif] {$ r $}复杂的解析函数定义的三网参数属于此类网络。三网## IMG ## {$ W（r，r，2）$ ...}的结构方程