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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.18097 |
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Table of Contents:
- 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.