%0 Journal Article
%T Hierarchies and compatibility on Courant algebroids
%A Paulo Antunes
%A Camille Laurent-Gengoux
%A Joana M. Nunes da Costa
%J Mathematics
%D 2011
%I arXiv
%X We extend to the context of Courant algebroids several hierarchies that can be constructed on Poisson-Nijenhuis manifolds. More precisely, we introduce several notions (Poisson-Nijenhuis, deformation-Nijenhuis and Nijenhuis pairs) that extend to Courant algebroids the notion of a Poisson-Nijenhuis manifold, by using the idea that both the Poisson and the Nijenhuis structures, although they seem to be different in nature when considered on manifolds, are just $(1,1)$-tensors on the usual Courant algebroid $TM \oplus T^*M $ satisfying several constraints. For each of the generalizations mentioned, we show that there are natural hierarchies obtained by successive deformation by one of the $(1,1)$-tensor.
%U http://arxiv.org/abs/1111.0800v2