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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A formula for the tangent bundle of flag manifolds and related manifolds


Author: Kee Yuen Lam
Journal: Trans. Amer. Math. Soc. 213 (1975), 305-314
MSC: Primary 57D20; Secondary 57F20
MathSciNet review: 0431194
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Abstract: A formula is given for the tangent bundle of a flag manifold G in terms of canonically defined vector bundles over G. The formula leads to a unified proof of some parallelizability theorems of Stiefel manifolds. It can also be used to deduce some immersion theorems for flag manifolds.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0431194-X
PII: S 0002-9947(1975)0431194-X
Keywords: Real, complex and quaternionic flag manifolds, tangent bundle, canonical vector bundles over flag manifolds, parallelizability of Stiefel manifolds, projective Stiefel manifolds, immersion of flag manifolds into Euclidean spaces
Article copyright: © Copyright 1975 American Mathematical Society