Commuting Vector Fields on S 3

1965 ◽  
Vol 81 (1) ◽  
pp. 70 ◽  
Author(s):  
Elon L. Lima
Keyword(s):  
Vector Fields ◽  
Commuting Vector Fields

The Equality of a Manifold's Rank and Dimension

1969 ◽  
Vol 12 (2) ◽  
pp. 183-184
Author(s):  
R. S. D. Thomas
Keyword(s):  
Vector Fields ◽  
Present Note ◽  
Linearly Independent ◽  
Commuting Vector Fields

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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