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Parallelizable manifold

In mathematics, a differentiable manifold M{\displaystyle M} of dimension n is called parallelizable if there exist smoothvector fields{V1,…,Vn}{\displaystyle \{V_{1},\ldots ,V_{n}\}} on the manifold, such that at every point p{\displaystyle p} of M{\displaystyle M} the tangent vectors{V1(p),…,Vn(p)}{\displaystyle \{V_{1}(p),\ldots ,V_{n}(p)\}} provide a basis of the tangent space at p{\displaystyle p}.

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