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arXiv · 2403.09152

Line geometry of pairs of second-order Hamiltonian operators and quasilinear systems

Giorgio Gubbiotti·Bert van Geemen·Pierandrea Vergallo
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Abstract

We demonstrate that a pair consisting of a second-order homogeneous Hamiltonian structure in $N$ components and its associated system of conservation laws is in bijective correspondence with an alternating three-form on a $N+2$-dimensional vector space. Additionally, we show that the three-form offers $N+2$ linear equations in the Pl\"ucker coordinates that define the associated line congruence. We utilize these results to characterize systems of conservation laws with second-order structure for $N\leq 4$. We finally comment how to extend this result for $N=6$.

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Giorgio Gubbiotti, Bert van Geemen, Pierandrea Vergallo. 2024-03-14. Line geometry of pairs of second-order Hamiltonian operators and quasilinear systems. https://arxiv.org/abs/2403.09152

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