The inhomogeneous transformation law for Christoffel symbols reflects their non-tensorial character, but the geodesic condition they define remains a diffeomorphism-invariant structural feature of the manifold.
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A mathematical object that describes physical quantities (like force or curvature) in a way that stays consistent no matter what coordinate system or perspective you use to measure it.
Transformation law(mathematics and physics)
A rule that describes how something changes when you switch to a different measurement system or coordinate system.
manifold(Kant's account of cognition in the Critique of Pure Reason)
The raw, unstructured multiplicity of content given in intuition prior to conceptual unification by the understanding