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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Integrably parallelizable manifolds


Author: Vagn Lundsgaard Hansen
Journal: Proc. Amer. Math. Soc. 35 (1972), 543-546
MSC: Primary 53C10; Secondary 57D15
DOI: https://doi.org/10.1090/S0002-9939-1972-0305296-5
MathSciNet review: 0305296
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Abstract: A smooth manifold $ {M^n}$ is called integrably parallelizable if there exists an atlas for the smooth structure on $ {M^n}$ such that all differentials in overlap between charts are equal to the identity map of the model for $ {M^n}$. We show that the class of connected, integrably parallelizable, n-dimensional smooth manifolds consists precisely of the open parallelizable manifolds and manifolds diffeomorphic to the n-torus.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0305296-5
Keywords: Tangent bundle, reduction of structural group, integrable reduction, parallelizable manifold, rank of a manifold
Article copyright: © Copyright 1972 American Mathematical Society