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.

Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds / Giovannardi G.. - In: ANALYSIS AND GEOMETRY IN METRIC SPACES. - ISSN 2299-3274. - STAMPA. - 8:(2020), pp. 68-91. [10.1515/agms-2020-0105]

Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds

Giovannardi G.
2020

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.
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68
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Giovannardi G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1284255
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