Abstract The deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

中文翻译：

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分级流形中规则子流形的高维完整映射

摘要 定阶子流形浸入分级流形中的变形条件可以表示为一阶偏微分方程系统。在规则子流形的特殊但重要的情况下，我们引入了坐标的自然选择，这允许深度简化系统的形式表达式，并将其简化为沿特征方向的 ODE 系统。我们引入了与一维情况类似的更高维完整映射的概念 [29]，并且我们提供了奇点的表征以及变形标准。