Integrably parallelizable manifolds

Hansen, Vagn Lundsgaard

doi:10.1090/S0002-9939-1972-0305296-5

Integrably parallelizable manifolds
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Proc. Amer. Math. Soc. 35 (1972), 543-546 Request permission

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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