VB-Courant Algebroids, E-Courant Algebroids and Generalized Geometry

Lang, Honglei ; Sheng, Yunhe ; Wade, Aïssa

Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 588-607

Résumé

In this paper, we first discuss the relation between $\text{VB}$ -Courant algebroids and $\text{E}$ -Courant algebroids, and we construct some examples of $\text{E}$ -Courant algebroids. Then we introduce the notion of a generalized complex structure on an $\text{E}$ -Courant algebroid, unifying the usual generalized complex structures on even-dimensional manifolds and generalized contact structures on odd-dimensional manifolds. Moreover, we study generalized complex structures on an omni-Lie algebroid in detail. In particular, we show that generalized complex structures on an omni-Lie algebra $\text{gl}\left( V \right)\oplus V$ correspond to complex Lie algebra structures on $V$ .

Détail

DOI : 10.4153/CMB-2017-079-7

Mots-clés : 53D17, 18B40, 58H05, VB-Courant algebroid, E-Courant algebroid, omni-Lie algebroid, generalized complex structure, algebroid-Nijenhuis structure

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