DUALITY OF (2, 3, 5)-DISTRIBUTIONS AND LAGRANGIAN CONE STRUCTURES
DUALITY OF (2, 3, 5)-DISTRIBUTIONS AND LAGRANGIAN CONE STRUCTURES
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(2,3,5)-分布的对偶性和拉格朗日锥结构
DOI：
10.1017/nmj.2019.46
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发表时间：
2018
影响因子：
0.8
通讯作者：
Wataru Yukuno
中科院分区：
文献类型：
--
作者：
G. Ishikawa;Y. Kitagawa;A. Tsuchida;Wataru Yukuno
正如部分作者所表明的，对于五维流形 $Y$ 上给定的 $(2,3,5)$-分布 $D$，在另一个五维流形 $X$ 上局部存在拉格朗日锥结构 $C$，该结构由 $(Y,D)$ 的异常或奇异路径组成。我们给出了对应于 $(2,3,5)$-分布的拉格朗日锥结构类的表征。因此，我们通过$G_{2}$类型的伪乘积结构完成了$(2,3,5)$分布和拉格朗日锥结构之间的对偶性。给出了对应于 $(2,3,5)$-分布的平坦拉格朗日锥结构全局模型的非平坦扰动的局部示例。
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.