Paraconformal geometry of nth order ODEs, and exotic holonomy in dimension four
نویسنده
چکیده
We characterise nth order ODEs for which the space of solutions M is equipped with a particular paraconformal structure in the sense of [2], that is a splitting of the tangent email [email protected] email [email protected]
منابع مشابه
Two Exotic Holonomies in Dimension Four , Path Geometries , and Twistor Theory
Since its introduction by Élie Cartan, the holonomy of a connection has played an important role in differential geometry. One of the best known results concerning holonomy is Berger’s classification of the possible holonomies of Levi-Civita connections of Riemannian metrics. Since the appearance of Berger [1955], much work has been done to refine his list of possible Riemannian holonomies. See...
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Bryant [Br] proved the existence of torsion free connections with exotic holonomy, i.e. with holonomy that does not occur on the classical list of Berger [Ber]. These connections occur on moduli spaces Y of rational contact curves in a contact threefold W. Therefore, they are naturally contained in the moduli space Z of all rational curves in W. We construct a connection on Z whose restriction ...
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تاریخ انتشار 2005