Isometry-invariant fibration

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Template:Fibration property

Template:Isometry-invariance property

Definition

Symbol-free definition

Given a manifold with a compatible Riemannian metric, a fibration from the manifold is said to be isometry-invariant if any isometry of the Riemannian manifold permutes the fibres of the fibration (viz preserves the equivalence relation of being in the same fibre).