As was shown by a part of the authors, for a given $(2,3,5)$-distribution $D$ on a five-dimensional manifold $Y$, there is, locally, a Lagrangian cone structure $C$ on another five-dimensional manifold $X$ which consists of abnormal or singular paths of $(Y,D)$. We give a characterization of the class of Lagrangian cone structures corresponding to $(2,3,5)$-distributions. Thus, we complete the duality between $(2,3,5)$-distributions and Lagrangian cone structures via pseudo-product structures of type $G_{2}$. A local example of nonflat perturbations of the global model of flat Lagrangian cone structure which corresponds to $(2,3,5)$-distributions is given.

中文翻译：

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(2, 3, 5)-分布和拉格朗日锥结构的对偶性

正如部分作者所表明的，对于给定的$(2,3,5)$-分配$D$在五维流形上$Y$, 局部存在拉格朗日锥结构$加元在另一个五维流形上$X$它由异常或奇异的路径组成$(Y,D)$. 我们给出了对应于的拉格朗日锥结构类的特征$(2,3,5)$-分布。因此，我们完成了之间的对偶$(2,3,5)$-分布和拉格朗日锥结构通过类型的伪积结构$G_{2}$. 平面拉格朗日锥结构的全局模型的非平面扰动的局部示例，对应于$(2,3,5)$-给出了分布。