DUALITY OF (2, 3, 5)-DISTRIBUTIONS AND LAGRANGIAN CONE STRUCTURES

As was shown by a part of the authors, for a given $(2,3,5)$-distribution $D$ on a five-dimensional manifold $Y$, there is, locally, a Lagrangian cone structure $C$ on another five-dimensional manifold $X$ which consists of abnormal or singular paths of $(Y,D)$. We give a characterization of the cla...

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Published inNagoya mathematical journal Vol. 243; pp. 303 - 315
Main Authors ISHIKAWA, GOO, KITAGAWA, YUMIKO, TSUCHIDA, ASAHI, YUKUNO, WATARU
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2021
Subjects
Control theory
Lie groups
Perturbation
53A55
53C17
53A20
70F25
58A30
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Summary:As was shown by a part of the authors, for a given $(2,3,5)$-distribution $D$ on a five-dimensional manifold $Y$, there is, locally, a Lagrangian cone structure $C$ on another five-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 nonflat perturbations of the global model of flat Lagrangian cone structure which corresponds to $(2,3,5)$-distributions is given.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0027-7630
2152-6842
DOI:10.1017/nmj.2019.46