Abstract:
In this paper introduce extended mirror Courant algebroids and their mirror Dirac structures on the vector bundle
\calE ^1\left( M \right)
. The extended mirror Courant bracket is the bracket corresponding to the standard extended Courant bracket on the vector bundle
\calE ^1\left( M \right)
via the vector bundle automorphism exchanging
\mathbbR
to
\mathbbR
. This paper is to study the algebraic geometry structures under the extend mirror Courant algebroids. We have found that the morphisms of the extended mirror Courant algebroids are the twisted and extennded mirror Courant algebroids, which are their respective twisted morphisms. Also provides a new idea for the study of Dirac bundle.