Gauge transformation of a manifold

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Symbol-free definition

A gauge transformation of a manifold is the gauge transformation of the tangent bundle of that manifold. In other words, it is a differentiable automorphism of the tangent bundle that sends the fiber over every point of the manifold to itself, and is a linear automorphism of each such fiber.

The term gauge transformation in general stands for the gauge transformation of a vector bundle, which is a more general concept.

The gauge group of a manifold is its group of gauge transformations.