Parallelizable
المؤلف:
Adams, J. F.
المصدر:
On the Non-Existence of Elements of Hopf Invariant One." Bull. Amer. Math. Soc. 64
الجزء والصفحة:
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14-8-2021
2531
Parallelizable
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).
More generally, an 
-dimensional manifold 
is parallelizable if its tangent bundle 
is a trivial bundle (i.e., if 
is globally of the form 
).
REFERENCES:
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.
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