VB-Courant algebroids, E-Courant algebroids and generalized geometry
Differential Geometry
2019-08-15 v2 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids and construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an 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 correspond to complex Lie algebra structures on V.
Cite
@article{arxiv.1705.10316,
title = {VB-Courant algebroids, E-Courant algebroids and generalized geometry},
author = {Honglei Lang and Yunhe Sheng and Aissa Wade},
journal= {arXiv preprint arXiv:1705.10316},
year = {2019}
}
Comments
19 pages