A Quaternionic Structure as a Landmark for Symplectic Maps

2019/10/29 by Hugo Jiménez-Pérez, Jiménez-Pérez, Hugo
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Geometric and Algebraic Topology #Mathematics and Applications #math-ph #math.MP #math.SG

paper · pdf · doi:10.48550/arxiv.1910.13031

7 pages, small modifications, some formulas corrected, we add some paragraphs about the application in symplectic integration

arxiv created 2020/10/22 · arxiv updated 2020/10/26

Abstract

We use a quaternionic structure on the product of two symplectic manifolds for relating Liouvillian forms with linear symplectic maps obtained by the symplectic Cayley's transformation.

Citations

• Symplectic manifolds and their lagrangian submanifolds

Related

• Symplectic maps: from generating functions to Liouvillian forms
• Fundaments of Quaternionic Clifford Analysis I
• Symplectic Geometry
• Generalized Quaternionic Manifolds
• Quaternionic-contact hypersurfaces