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.
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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