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BY 4.0 license Open Access Published by De Gruyter Open Access July 1, 2020

Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds

  • Gianmarco Giovannardi


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.

MSC 2010: 58H99; 49Q99; 58A17


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Received: 2019-01-23
Accepted: 2020-04-23
Published Online: 2020-07-01

© 2020 Gianmarco Giovannardi, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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