2023/12/05 by Yuji Hirota, Hirota, Yuji, Noriaki Ikeda +1
Mathematics · Physics and Astronomy · #53D05 (Secondary) #53D20 (Primary) #Advanced Differential Geometry Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2312.02499
openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study multisymplectic structures taking values in vector bundles with connections from the viewpoint of the Hamiltonian symmetry. We introduce the notion of bundle-valued n-plectic structures and exhibit some properties of them. In addition, we define bundle-valued homotopy momentum sections for bundle-valued n-plectic manifolds with Lie algebroids to discuss momentum map theories in both cases of quaternionic Kähler manifolds and hyper-Kähler manifolds. Furthermore, we generalize the Marsden-Weinstein-Meyer reduction theorem for symplectic manifolds and construct two kinds of reductions of vector-valued 1-plectic manifolds.