Displaying similar documents to “ Horizontal lift of symmetric connections to the bundle of volume forms ν ”

Affine analogues of the Sasaki-Shchepetilov connection

Maria Robaszewska (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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For two-dimensional manifold M with locally symmetric connection ∇ and with ∇-parallel volume element vol one can construct a flat connection on the vector bundle TM ⊕ E, where E is a trivial bundle. The metrizable case, when M is a Riemannian manifold of constant curvature, together with its higher dimension generalizations, was studied by A.V. Shchepetilov [J. Phys. A: 36 (2003), 3893-3898]. This paper deals with the case of non-metrizable locally symmetric connection. Two flat connections...

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.