Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition
Given a maximally non-integrable 2-distribution D on a 5-manifold M, it was discovered by P. Nurowski that one can naturally associate a conformal structure [g]D of signature (2,3) on M. We show that those conformal structures [g]D which come about by this construction are characterized by the exist...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2009 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2009
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149138 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition / M. Hammerl, K. Sagerschnig // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 41 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862643437689372672 |
|---|---|
| author | Hammerl, M. Sagerschnig, K. |
| author_facet | Hammerl, M. Sagerschnig, K. |
| citation_txt | Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition / M. Hammerl, K. Sagerschnig // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Given a maximally non-integrable 2-distribution D on a 5-manifold M, it was discovered by P. Nurowski that one can naturally associate a conformal structure [g]D of signature (2,3) on M. We show that those conformal structures [g]D which come about by this construction are characterized by the existence of a normal conformal Killing 2-form which is locally decomposable and satisfies a genericity condition. We further show that every conformal Killing field of [g]D can be decomposed into a symmetry of D and an almost Einstein scale of [g]D.
|
| first_indexed | 2025-12-01T08:11:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149138 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T08:11:43Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hammerl, M. Sagerschnig, K. 2019-02-19T17:37:41Z 2019-02-19T17:37:41Z 2009 Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition / M. Hammerl, K. Sagerschnig // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 41 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 34A26; 35N10; 53A30; 53B15; 53B30 https://nasplib.isofts.kiev.ua/handle/123456789/149138 Given a maximally non-integrable 2-distribution D on a 5-manifold M, it was discovered by P. Nurowski that one can naturally associate a conformal structure [g]D of signature (2,3) on M. We show that those conformal structures [g]D which come about by this construction are characterized by the existence of a normal conformal Killing 2-form which is locally decomposable and satisfies a genericity condition. We further show that every conformal Killing field of [g]D can be decomposed into a symmetry of D and an almost Einstein scale of [g]D. This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”. We cannot underestimate the value of discussions with Andreas Cap on various technical procedures used in this paper. The concept of orbit types of parallel tractors was introduced to the first author by Felipe Leitner, who moreover suggested to check for simplicity of the underlying 2-form. We thank the referees for their careful reading and various valuable suggestions for improvements. The first author was supported by the IK I008-N funded by the University of Vienna. The second author was supported by project P 19500-N13 of the “Fonds zur F¨orderung der wissenschaftlichen Forschung” (FWF). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition Article published earlier |
| spellingShingle | Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition Hammerl, M. Sagerschnig, K. |
| title | Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition |
| title_full | Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition |
| title_fullStr | Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition |
| title_full_unstemmed | Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition |
| title_short | Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition |
| title_sort | conformal structures associated to generic rank 2 distributions on 5-manifolds – characterization and killing-field decomposition |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149138 |
| work_keys_str_mv | AT hammerlm conformalstructuresassociatedtogenericrank2distributionson5manifoldscharacterizationandkillingfielddecomposition AT sagerschnigk conformalstructuresassociatedtogenericrank2distributionson5manifoldscharacterizationandkillingfielddecomposition |