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 a graded manifold can be expressed as a system of first order citronella horse shampoo 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, here 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.