On the geometry of complex Poisson bivectors
Symplectic Geometry
2025-06-24 v1
Abstract
We study the geometry of complex Poisson bivectors over smooth manifolds. We show that under mild regularity conditions any complex Poisson bivector has associated a complex presymplectic foliation. After that, we use techniques of Dirac geometry to provide a more concise description of this complex presymplectic foliation. Moreover, we introduce two new classes of structures: quasi-real Poisson and quasi-real Dirac structures. In the last part, we focus on the normal form of complex Poisson bivectors. Under certain regularity, we provide a normal form theorem for complex Poisson structures along certain kinds of submanifolds.
Cite
@article{arxiv.2506.18097,
title = {On the geometry of complex Poisson bivectors},
author = {Dan Aguero},
journal= {arXiv preprint arXiv:2506.18097},
year = {2025}
}