E-Courant Algebroids

In this paper, we introduce the notion of E-Courant algebroids, where E is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Courant–Jacobi algebroids and omni-Lie algebroids as its special cases. We explore novel phenomena exhibited by E-Courant algebroids and provide many examples. We study the automorphism groups of omni-Lie algebroids and classify the isomorphism classes of exact E-Courant algebroids. In addition, we introduce the concepts of E-Lie bialgebroids and Manin triples.