English

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 \gl(V)V\gl(V)\oplus V correspond to complex Lie algebra structures on V.

Keywords

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

R2 v1 2026-06-22T20:02:33.990Z