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 singular paths for (2,3,5)-distributions
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abstract
We show a duality which arises from distributions of Cartan type, having growth (2, 3, 5), from the view point of geometric control theory. In fact we consider the space of singular (or abnormal) paths on a given five dimensional space endowed with a Cartan distribution, which form another five dimensional space with a cone structure. We regard the cone structure as a control system and show that the space of singular paths of the cone structure is naturally identified with the original space. Moreover we observe an asymmetry on this duality in terms of singular paths.
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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.