Integrably parallelizable manifolds
HTML articles powered by AMS MathViewer
- by Vagn Lundsgaard Hansen PDF
- 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.References
- A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. III, Amer. J. Math. 82 (1960), 491–504. MR 120664, DOI 10.2307/2372969
- J. Eells and K. D. Elworthy, Open embeddings of certain Banach manifolds, Ann. of Math. (2) 91 (1970), 465–485. MR 263120, DOI 10.2307/1970634
- A. Haefliger, Lectures on the theorem of Gromov, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Lecture Notes in Math., Vol. 209, Springer, Berlin, 1971, pp. 128–141. MR 0334241
- Noel J. Hicks, Notes on differential geometry, Van Nostrand Mathematical Studies, No. 3, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. MR 0179691
- Morris W. Hirsch, On imbedding differentiable manifolds in euclidean space, Ann. of Math. (2) 73 (1961), 566–571. MR 124915, DOI 10.2307/1970318
- Nicolaas H. Kuiper, The homotopy type of the unitary group of Hilbert space, Topology 3 (1965), 19–30. MR 179792, DOI 10.1016/0040-9383(65)90067-4
- Harold Rosenberg, Actions of $R^{n}$ on manifolds, Comment. Math. Helv. 41 (1966/67), 170–178. MR 206978, DOI 10.1007/BF02566874
- T. J. Willmore, Connexions for systems of parallel distributions, Quart. J. Math. Oxford Ser. (2) 7 (1956), 269–276. MR 97832, DOI 10.1093/qmath/7.1.269
Additional Information
- © Copyright 1972 American Mathematical Society
- 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