Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds
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...
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-07-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.1515/agms-2020-0105 |
| _version_ | 1818681878316580864 |
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| author | Giovannardi Gianmarco |
| author_facet | Giovannardi Gianmarco |
| author_sort | Giovannardi Gianmarco |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T10:09:57Z |
| format | Article |
| id | doaj.art-15602434fd0449d1b0411802bb34175c |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-17T10:09:57Z |
| publishDate | 2020-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-15602434fd0449d1b0411802bb34175c2022-12-21T21:53:02ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742020-07-0181689110.1515/agms-2020-0105agms-2020-0105Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded ManifoldsGiovannardi Gianmarco0University of Bologna, Bologna, ItalyThe 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.https://doi.org/10.1515/agms-2020-0105sub-riemannian manifoldsgraded manifoldsregular and singular ruled submanifoldshigher-dimensional holonomy mapadmissible variations58h9949q9958a17 |
| spellingShingle | Giovannardi Gianmarco Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds Analysis and Geometry in Metric Spaces sub-riemannian manifolds graded manifolds regular and singular ruled submanifolds higher-dimensional holonomy map admissible variations 58h99 49q99 58a17 |
| title | Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds |
| title_full | Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds |
| title_fullStr | Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds |
| title_full_unstemmed | Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds |
| title_short | Higher Dimensional Holonomy Map for Ruled Submanifolds in Graded Manifolds |
| title_sort | higher dimensional holonomy map for ruled submanifolds in graded manifolds |
| topic | sub-riemannian manifolds graded manifolds regular and singular ruled submanifolds higher-dimensional holonomy map admissible variations 58h99 49q99 58a17 |
| url | https://doi.org/10.1515/agms-2020-0105 |
| work_keys_str_mv | AT giovannardigianmarco higherdimensionalholonomymapforruledsubmanifoldsingradedmanifolds |