On the geometry of chains

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14410%2F09%3A00029292" target="_blank" >RIV/00216224:14410/09:00029292 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On the geometry of chains

Popis výsledku v původním jazyce

The chains studied here form a canonical family of paths in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be encoded as Cartan geometries. The aim of this paper is to study the relation between these two Cartan geometries for Lagrangean contact and almost CR structures by a general method of extending Cartan geometries. We show the canonical Cartan geometry associated to the family of chains can be obtained in that way if and onlyif the original parabolic contact structure is torsion free. In that case, the Cartan curvature associated to the family of chains is carefully analyzed. In the end, this allows to prove the underlying torsion free parabolic contact structure can be (almost) recovered just from its chains. In particular, this leads to a very conceptual proof of the fact that chain preserving contact diffeomorphisms are either isomorphisms or anti-isomorphisms of the structure.

Název v anglickém jazyce

On the geometry of chains

Popis výsledku anglicky

The chains studied here form a canonical family of paths in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be encoded as Cartan geometries. The aim of this paper is to study the relation between these two Cartan geometries for Lagrangean contact and almost CR structures by a general method of extending Cartan geometries. We show the canonical Cartan geometry associated to the family of chains can be obtained in that way if and onlyif the original parabolic contact structure is torsion free. In that case, the Cartan curvature associated to the family of chains is carefully analyzed. In the end, this allows to prove the underlying torsion free parabolic contact structure can be (almost) recovered just from its chains. In particular, this leads to a very conceptual proof of the fact that chain preserving contact diffeomorphisms are either isomorphisms or anti-isomorphisms of the structure.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F05%2F2117" target="_blank" >GA201/05/2117: Algebraické metody v topologii a geometrii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Geometry

ISSN

0022-040X

e-ISSN

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Svazek periodika

82

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

33

Strana od-do

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Kód UT WoS článku

000266917200001

EID výsledku v databázi Scopus

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