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The Equality of a Manifold's Rank and Dimension
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1969