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arXiv math/0010178math.DG
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子网可约的多维(n+1)-网

Multidimensional (n+1)-Webs with Reduct Reducible Subwebs

Vladislav V. Goldberg

摘要:

我们发现了具有约化可约子网的多维(n+1)-网W的三个特征:它的封闭形式方程,与W相关的不变分布的可积性,以及它的挠率张量分量之间的关系.在余维1的情况下,后者的标准建立了一个非线性二阶偏微分方程系统的解决方案的关系。Goursat在1899年考虑了这个系统的一些特殊情况。

英文摘要:

We find three characterizations for a multidimensional (n+1)-web W possessing a reduct reducible subweb: its closed form equations, the integrability of an invariant distribution associated with W, and the relations between the components of its torsion tensor. In the case of codimension one, the latter criterion establishes a relation with solutions of a system of nonlinear second-order PDEs. Some particular cases of this system were considered by Goursat in 1899.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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