Compatibility between an almost Dirac structure and a connection [Compatibilité d'un fibré de Dirac avec une connexion]

摘要

We extend to an almost Dirac structure and affine connections the notion of compatibility of a bivectors field or a 2-differential form with a pseudo-metric. Compatibility with a symmetric connection implies integrability. We shall be interested especially by such structures on Lie groups or Riemannian homogeneous spaces.