On the affine connections that give rise to a given curvature
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A problem of both theoretical and practical importance is that of characterizing the collection of all affine connections that gives rise to a given curvature structure on a subset of a differentiable manifold of finite dimension. This problem is solved in closed form in Section three. We also show that the cardinality of the collection of all distinct connections that give the same curvature is that of the continuum, and that the connections of any two curvature structures can be brought into a1-to-1 correspondence.
KeywordsClosed Form Practical Importance Finite Dimension Differentiable Manifold Curvature Structure
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