  In this paper, we show that associated to any coisotropic Cartan geometry
there is a twisted Courant algebroid. This includes in particular parabolic
geometries. Using this twisted Courant structure, we give some new results
about the Cartan curvature and the Weyl structure of a parabolic geometry. As
more direct applications, we have Lie 2-algebra and 3D AKSZ sigma model with
background associated to any coisotropic Cartan geometry.
