In differential geometry, a pullback refers to the operation that takes a differential form defined on a manifold and allows it to be transported back to another manifold via a smooth map. This concept is crucial for understanding how properties of one manifold can relate to another, particularly when dealing with smooth manifolds, induced metrics on submanifolds, and conformal metrics. The pullback essentially enables us to analyze forms and functions in the context of their original manifolds, facilitating the study of geometric structures.
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