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    The conformal structure, combined with a volume element (... — Carmelics
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    Challenges→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.

    The conformal structure, combined with a volume element (i.e., a choice of compatible metric determinant), suffices to single out a unique torsion-free connection without invoking additional geometric structure.

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    Key Terms

    Geometric structure(in mathematics and physics)
    The underlying mathematical properties and rules that define how a space is organized and how things relate to each other within it.
    Metric determinant(in differential geometry)
    A number that comes from a metric (a way of measuring distances) and tells you important information about how distances work in that space.
    Torsion-free connection(in differential geometry)
    A rule for how to move and compare directions smoothly through a curved space without any 'twisting' or distortion.
    Volume element(in geometry)
    A mathematical tool that lets you measure the size or 'amount of space' in a region, similar to how you'd measure the volume of a box.
    conformal structure

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    (Weyl's infinitesimal geometry)
    A geometric structure on a manifold that determines only an equivalence class of conformally equivalent symmetric linear connections, not a unique affine connection.

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    An additional structure beyond the conformal structure is required in order to d...

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