Generalized contact bundles

Luca Vitagliano; Aïssa Wade

doi:10.1016/j.crma.2015.12.009

Differential geometry

Generalized contact bundles

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2015-07-14
Accepted: 2015-12-14
Published online: 2016-02-04

DOI: 10.1016/j.crma.2015.12.009

Author's affiliations:

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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