A hypersphere is parallelizable if there are vector fields that are linearly
independent at each point. There exist only three parallelizable spheres: , , and (Adams 1958, 1960, Le Lionnais 1983).
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J. F. "On the Non-Existence of Elements of Hopf Invariant One." Ann.
Math.72, 20-104, 1960.Le Lionnais, F. Les
nombres remarquables. Paris: Hermann, p. 49, 1983.Wald,
R. M. General
Relativity. Chicago, IL: University of Chicago Press, 1984.