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).
Adams, J. F. "On the Non-Existence of Elements of Hopf Invariant One." Bull. Amer. Math. Soc.64, 279-282, 1958.Adams,
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.
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).
-dimensional
manifold 
is parallelizable if its tangent
bundle 
is a trivial bundle (i.e., if 
is globally of the form 
).
