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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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- Research Article
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- Copyright © Canadian Mathematical Society 1969
References
1.
Willmore, T.J., Connexions for systems of parallel distributions. Quart. J. Math. Oxford (2) 7 (1956) 269–276.Google Scholar
2.
Gottschalk, W. H. and Hedlund, G. A., Topological dynamics. American Mathematical Society Colloquium Publications Volume XXXVI Providence, R.I., 1955.Google Scholar
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