Canonical Torsion-Free Connections on the Total Space of the Tangent and the Cotangent Bundle

Details Canonical Torsion-Free Connections on the Total Space of the Tangent and the Cotangent Bundle Canonical Torsion-Free Connections on the Total Space of the Tangent and the Cotangent Bundle

2009-04-29

arxiv.org/abs/0904.4581v1

Mathematics

Representation Theory

Scientific paper

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.

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