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 
). 