Definition:Tangent Bundle

Definition

Let $M$ be a differentiable manifold.

Let $p \in M$ be a point in $M$.

Let $T_p M$ be the tangent space at $p$.

The tangent bundle of $M$ is the disjoint union of all the tangent spaces of $M$:

$\ds T M = \coprod_{p \mathop \in M} T_p M$

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Also see

• Tangent Bundle is Differential Manifold

• Results about tangent bundles can be found here.

Sources

• 2003: John M. Lee: Introduction to Smooth Manifolds: $\S 3$: Tangent Vectors. The Tangent Bundle