Displaying similar documents to “On the curvature of tensor product connections and covariant differentials”

Horizontal lift of symmetric connections to the bundle of volume forms ν

Anna Gąsior (2010)

Annales UMCS, Mathematica

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In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms ν and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a F(3, 1)-structure on ν.

Reduction theorem for general connections

Josef Janyška (2011)

Annales Polonici Mathematici

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We prove the (first) reduction theorem for general and classical connections, i.e. we prove that any natural operator of a general connection Γ on a fibered manifold and a classical connection Λ on the base manifold can be expressed as a zero order operator of the curvature tensors of Γ and Λ and their appropriate derivatives.