no. 3
Differential geometry
Generalized contact bundles
[Sur le fibrés de contact généralisés]

Présenté par : Charles-Michel Marle

Vitagliano, Luca1 ; Wade, Aïssa2
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, Tome 354 (2016) no. 3, pp. 313-317.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.12.009
Vitagliano, Luca 1 ; Wade, Aïssa 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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Vitagliano, Luca; Wade, Aïssa. Generalized contact bundles. Comptes Rendus. Mathématique, Tome 354 (2016) no. 3, pp. 313-317. doi : 10.1016/j.crma.2015.12.009. http://www.numdam.org/articles/10.1016/j.crma.2015.12.009/

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