Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds

Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds

Blog Article

The deformability condition for submanifolds of fixed degree immersed in 15-eg2373cl 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 korpskaft for singularities as well as a deformability criterion.