Geodesic
VB-Courant Algebroids, E-Courant Algebroids and Generalized Geometry
Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 588-607

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DOI

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 $V$ .
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 
Lang, Honglei; Sheng, Yunhe; Wade, Aïssa. VB-Courant Algebroids, E-Courant Algebroids and Generalized Geometry. Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 588-607. doi: 10.4153/CMB-2017-079-7
@article{10_4153_CMB_2017_079_7,
     author = {Lang, Honglei and Sheng, Yunhe and Wade, A{\"\i}ssa},
     title = {VB-Courant {Algebroids,} {E-Courant} {Algebroids} and {Generalized} {Geometry}},
     journal = {Canadian mathematical bulletin},
     pages = {588--607},
     year = {2018},
     volume = {61},
     number = {3},
     doi = {10.4153/CMB-2017-079-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-079-7/}
}
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%J Canadian mathematical bulletin
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