 Parallelizable manifold

A **parallelizable manifold** is a differentiable manifold that has a global frame of vector fields. This means there exists a set of smooth vector fields that span the tangent space at every point of the manifold, and these vector fields can be chosen to vary smoothly. In more formal terms, a manifold \( M \) is said to be parallelizable if there exists a smooth bundle of vector fields \( \{V_1, V_2, ...