CANONICAL TORSION-FREE CONNECTIONS ON THE TOTAL SPACE OF THE TANGENT AND THE COTANGENT BUNDLE

Lionel Bérard Bergery (1) , Thomas Krantz (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 URMUL - Unité de Recherche en Mathématiques

In this paper we define a class of torsion-free connections on the total space of the (co-)tangent bundle over a base-manifold with a connection and for which tangent spaces to the fibers are parallel. Each tangent space to a fiber is flat for these connections and the canonical projection from the (co-)tangent bundle to the base manifold is totally geodesic. In particular cases the connection is metric with signature (n,n) or symplectic and admits a single parallel totally isotropic tangent n-plane.

Mots clés: connection; holonomy; vector bundle

Domaines: Théorie des représentations [math.RT]

Lionel Bérard Bergery, Thomas Krantz. CANONICAL TORSION-FREE CONNECTIONS ON THE TOTAL SPACE OF THE TANGENT AND THE COTANGENT BUNDLE. 2009. ⟨hal-00267590v4⟩