Dirac structures and Nijenhuis operators
Differential Geometry
2023-05-05 v1 Symplectic Geometry
Abstract
We introduce a notion of compatibility between (almost) Dirac structures and (1,1)-tensor fields extending that of Poisson-Nijenhuis structures. We study several properties of the "Dirac-Nijenhuis" structures thus obtained, including their connection with holomorphic Dirac structures, the geometry of their leaves and quotients, as well as the presence of hierarchies. We also consider their integration to Lie groupoids, which includes the integration of holomorphic Dirac structures as a special case.
Keywords
Cite
@article{arxiv.2109.06330,
title = {Dirac structures and Nijenhuis operators},
author = {Henrique Bursztyn and Thiago Drummond and Clarice Netto},
journal= {arXiv preprint arXiv:2109.06330},
year = {2023}
}
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35 pages