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Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition
Інший ID:
2000 Mathematics Subject Classification: 34A26; 35N10; 53A30; 53B15; 53B30
Посилання:
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.
Підтримка:
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).
Дата:
2009
Переглядів:
466
Завантажень:
206
Анотація:
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.
