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    A unique symmetric linear connection cannot be selected f... — Carmelics
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    Home/Modality & Possibility
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    Supports→An additional structure beyond the conformal structure is required in order to determine a unique symmetric linear connection from the equivalence class of conformally equivalent symmetric linear connections.

    A unique symmetric linear connection cannot be selected from the equivalence class without additional information.

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    An additional structure beyond the conformal structure is required in order to d...The conformal structure alone determines only an equivalence class of conformall...Weyl's fundamental principle of infinitesimal geometry requires that the metric ...

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    An additional structure beyond the conformal structure is required in ...85%The geometry determines a unique, symmetric, linear connection Γ84%The metric uniquely determines the symmetric linear connection.83%A conformal structure determines only an equivalence class of conforma...82%

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    Since the conformal structure determines only an equivalence class of conformally equivalent symmetric linear connections \(K = [\Gamma]\), the affine connection in this type of geometry is not uniquely determined, and the parallel transport of vectors is not generally well defined. Moreover, the ratio of the lengths of two vectors located at different points is not determined even in a path-dependent way. According to Weyl, it is a fundamental principle of infinitesimal geometry that the metric

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