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EnglishWe investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. % Examples include equations of associativity of two-dimensional topological % field theory (WDVV equations). and various equations of Monge-Amp`ere % type. The classification of such systems is reduced to the projective classification of linear congruences of lines in $mathbb{P}^{n+2}$ satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space $W$ of dimension $n+2$, classify $n$-tuples of skew-symmetric 2-forms $A^{alpha} in Lambda^2(W)$ such that $$ phi_{eta gamma}A^{eta}wedge A^{gamma}=0, $$ for some non-degenerate symmetric $phi$.
| Titolo: | Systems of conservation laws with third-order Hamiltonian structures |
| Autori: | VITOLO, Raffaele (Corresponding) |
| Data di pubblicazione: | 2018 |
| Rivista: | |
| Abstract: | We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. % Examples include equations of associativity of two-dimensional topological % field theory (WDVV equations). and various equations of Monge-Amp`ere % type. The classification of such systems is reduced to the projective classification of linear congruences of lines in $mathbb{P}^{n+2}$ satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space $W$ of dimension $n+2$, classify $n$-tuples of skew-symmetric 2-forms $A^{alpha} in Lambda^2(W)$ such that $$ phi_{eta gamma}A^{eta}wedge A^{gamma}=0, $$ for some non-degenerate symmetric $phi$. |
| Handle: | http://hdl.handle.net/11587/417408 |
| Appare nelle tipologie: | Articolo pubblicato su Rivista |
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