Geodesic
The Equality of a Manifold's Rank and Dimension
Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 183-184

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T. J. Willmore has shown that if a differentiable manifold's rank (the maximum number of everywhere linearly independent commuting vector fields definable on it) equals the manifold's dimension, then the manifold is a torus of the appropriate dimension [1]. This theorem is proved more simply and without any differentiability hypothesis in the present note. 
Thomas, R. S. D. The Equality of a Manifold's Rank and Dimension. Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 183-184. doi: 10.4153/CMB-1969-019-8
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