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arXiv · 1906.05033

Higher dimensional holonomy map for ruled submanifolds in graded manifolds

Gianmarco Giovannardi
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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 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 [J. Differential Geom., 36(3):551-589, 1992], and we provide a characterization for singularities as well as a deformability criterion.

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Gianmarco Giovannardi. 2019-06-12. Higher dimensional holonomy map for ruled submanifolds in graded manifolds. https://doi.org/10.1515/agms-2020-0105

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