Generalized contact bundles

Luca Vitagliano; Aïssa Wade

doi:10.1016/j.crma.2015.12.009

Differential geometry

Generalized contact bundles
[Sur le fibrés de contact généralisés]

Présenté par : Charles-Michel Marle

Luca Vitagliano ¹ ; Aïssa Wade ²

¹ DipMat, Università degli Studi di Salerno & Istituto Nazionale di Fisica Nucleare, GC Salerno, via Giovanni Paolo II n
² Department of Mathematics, Penn State University, University Park, State College, PA 16802, USA

Comptes Rendus. Mathématique, Volume 354 (2016) no. 3, pp. 313-317.

Résumé
Abstract

Dans cette Note, nous proposons une approche des structures de contact généralisées reposant sur les fibrés vectoriels de rang 1. Cette nouvelle approche possède trois principaux avantages : (1) elle inclut toutes les autres approches connues à ce jour ; (2) elle éclaircit la signification géométrique de la condition d'intégrabilité des structures de contact généralisées ; (3) au vu de résultats récents obtenus sur les formes multiplicatives et les opérateurs de Spencer [8], elle permet une interprétation simple des équations définissant une structure généralisée de contact en termes d'algébroïdes et de groupoïdes de Lie.

In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of the integrability condition for generalized contact structures; (3) in light of new results on multiplicative forms and Spencer operators [8], it allows a simple interpretation of the defining equations of a generalized contact structure in terms of Lie algebroids and Lie groupoids.

Reçu le : 2015-07-14
Accepté le : 2015-12-14
Publié le : 2016-02-04

DOI : 10.1016/j.crma.2015.12.009

Affiliations des auteurs :

Luca Vitagliano ¹ ; Aïssa Wade ²

¹ DipMat, Università degli Studi di Salerno & Istituto Nazionale di Fisica Nucleare, GC Salerno, via Giovanni Paolo II n
² Department of Mathematics, Penn State University, University Park, State College, PA 16802, USA

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     author = {Luca Vitagliano and A{\"\i}ssa Wade},
     title = {Generalized contact bundles},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {313--317},
     publisher = {Elsevier},
     volume = {354},
     number = {3},
     year = {2016},
     doi = {10.1016/j.crma.2015.12.009},
     language = {en},
}

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Luca Vitagliano; Aïssa Wade. Generalized contact bundles. Comptes Rendus. Mathématique, Volume 354 (2016) no. 3, pp. 313-317. doi : 10.1016/j.crma.2015.12.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.12.009/

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