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The vector bundle whose fiber at each point is the tangent space of a smooth manifold.
wp-tangent_bundlenlab-tangent_bundleEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Each smooth manifold canonically determines its tangent bundle.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-tangent_bundlenlab-tangent_bundleEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The cotangent bundle is the fiberwise dual of the tangent bundle.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-cotangent_bundlenlab-cotangent_bundleThis is an authored directed relation from the source endpoint to the target endpoint.
Tensor powers and duals of tangent bundles form tensor bundles.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-tensor_bundlenlab-vector-bundle