= Tangent bundle
{wiki=Tangent_bundle}
In differential geometry, the tangent bundle is a fundamental construction that enables the study of the properties of differentiable manifolds. It provides a way to associate a vector space (the tangent space) to each point of a manifold, facilitating the analytical treatment of curves, vector fields, and differential equations. \#\#\# Definition: For a differentiable manifold \\( M \\), the tangent bundle \\( TM \\) is defined as the collection of all tangent spaces at each point of \\( M \\).
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