Differential Geometry
Hypercomplex structures on Courant algebroids

Presented by: Charles-Michel Marle

Stiénon, Mathieu1, 2
1 Université Paris Diderot, Institut de mathématiques de Jussieu (UMR CNRS 7586), site Chevaleret, case 7012, 75205 Paris cedex 13, France
2 Pennsylvania State University, Department of Mathematics, 109, McAllister Building, University Park, PA 16802, United States
Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 545-550.

Hypercomplex structures on Courant algebroids unify holomorphic symplectic structures and usual hypercomplex structures. In this Note, we prove the equivalence of two characterizations of hypercomplex structures on Courant algebroids, one in terms of Nijenhuis concomitants and the other in terms of (almost) torsionfree connections for which each of the three complex structures is parallel.

Les structures hypercomplexes sur les algébroïdes de Courant unifient les structures symplectiques holomorphes et les structures hypercomplexes usuelles. Dans cette Note, nous prouvons l'équivalence de deux caractérisations des structures hypercomplexes sur les algébroïdes de Courant, l'une en termes de concomitants de Nijenhuis et l'autre en termes de connexions (presque) sans torsion pour lesquelles les trois structures complexes sont parallèles.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.02.020
Stiénon, Mathieu 1, 2

1 Université Paris Diderot, Institut de mathématiques de Jussieu (UMR CNRS 7586), site Chevaleret, case 7012, 75205 Paris cedex 13, France
2 Pennsylvania State University, Department of Mathematics, 109, McAllister Building, University Park, PA 16802, United States 
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Stiénon, Mathieu. Hypercomplex structures on Courant algebroids. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 545-550. doi : 10.1016/j.crma.2009.02.020. http://www.numdam.org/articles/10.1016/j.crma.2009.02.020/

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