Prolongations of (3,6)-distributions by singular curves establish equivalences among the classification problems for (3,6), (3,5,7,8), (3,5,7,8,9) with pseudo-product structure, and (4,6,8)-distributions, generalizing B3-SO(3,4) homogeneous models.
Duality of (2,3,5)-distributions and Lagrangian cone structures
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abstract
As was shown by a part of the authors, for a given $(2, 3, 5)$-distribution $D$ on a $5$-dimensional manifold $Y$, there is, locally, a Lagrangian cone structure $C$ on another $5$-dimensional manifold $X$ which consists of abnormal or singular paths of $(Y, D)$. We give a characterization of the class of Lagrangian cone structures corresponding to $(2, 3, 5)$-distributions. Thus we complete the duality between $(2, 3, 5)$-distributions and Lagrangian cone structures via pseudo-product structures of type $G_2$. A local example of non-flat perturbations of the global model of flat Lagrangian cone structure which corresponds to $(2,3,5)$-distributions is given.
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math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Prolongations of $(3, 6)$-distributions by singular curves
Prolongations of (3,6)-distributions by singular curves establish equivalences among the classification problems for (3,6), (3,5,7,8), (3,5,7,8,9) with pseudo-product structure, and (4,6,8)-distributions, generalizing B3-SO(3,4) homogeneous models.