Duality of singular paths for (2,3,5)-distributions

2013/08/12 by Goo Ishikawa, Ishikawa, Goo, Yumiko Kitagawa +3
Mathematics · #53A55 #53C17 #58A30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A55 #msc:53C17 #msc:58A30

paper · pdf · doi:10.48550/arxiv.1308.2501

17 pages, no figures

arxiv created 2013/08/12 · arxiv updated 2013/08/13

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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