Corpus ID: 119578618

Integrable systems in 4D associated with sixfolds in Gr(4,6)

@article{Doubrov2017IntegrableSI,
  title={Integrable systems in 4D associated with sixfolds in Gr(4,6)},
  author={B. Doubrov and E. Ferapontov and B. Kruglikov and V. Novikov},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2017}
}
Let $Gr(d,n)$ be the Grassmannian of $d$-dimensional linear subspaces of an $n$-dimensional vector space $V$. A submanifold $X\subset Gr(d, n)$ gives rise to a differential system $\Sigma(X)$ that governs $d$-dimensional submanifolds of $V$ whose Gaussian image is contained in $X$. We investigate a special case of this construction where $X$ is a sixfold in $Gr(4, 6)$. The corresponding system $\Sigma(X)$ reduces to a pair of first-order PDEs for 2 functions of 4 independent variables… Expand

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