Parallelizable manifold

In mathematics, a differentiable manifold M {displaystyle M} of dimension n is called parallelizable if there exist smooth vector fields In mathematics, a differentiable manifold M {displaystyle M} of dimension n is called parallelizable if there exist smooth vector fields on the manifold, such that at every point p {displaystyle p} of M {displaystyle M} the tangent vectors provide a basis of the tangent space at p {displaystyle p} . Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a global section on M . {displaystyle M.} A particular choice of such a basis of vector fields on M {displaystyle M} is called a parallelization (or an absolute parallelism) of M {displaystyle M} .