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Hamiltonian dynamics and geometry on the two-plectic six-sphere

Year: 2026

Type: article

Abstract: We study the two-plectic geometry of the six-sphere induced by pulling back a canonical $G_2$-invariant three-form from $\mathbb{R}^7$. Notably we explicitly prove non-flatness of this structure and show that its infinitesimal automorphisms are given by the exceptional Lie algebra $\mathfrak{g}_2$. Several interesting classes of solutions of the dynamical Hamilton-de Donder-Weyl equations with one- and two-dimensional sources are exhibited.

Source: Journal of Symplectic Geometry

DOI: 10.4310/jsg.260824013507

Authors: Maxime Wagner, Tilmann Wurzbacher

Institutions: Centre National de la Recherche Scientifique, Institut Élie Cartan de Lorraine

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4407124091

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