Immersions of Complex Flagmanifolds.

Some embeddings of Lie groups in Euclidean space

“…Note that we have only used Tornehave's result to reduce the embedding codimension by /, so that we have re-proved the result of Borel and Hirzebruch [1] that G/T is always stably parallelizable. (In [10], Tornehave also proved this result in an elementary fashion. )…”

“…(G), of G, one obtains a well known embedding G/T -* Z£(G) where T is a maximal torus of G (T is the centralizer of x 0 ). In [10], Tornehave shows that this embedding has trivial normal bundle. One can use this embedding and some [MATHEMATIKA 18 (1971), [152][153][154][155][156] information about the bundle G -+ G/T to obtain an embedding of G in Euclidean space.…”

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

“…Remark. The immersion of complex flag manifolds is obtained by Tornehave [11], using a quite different method. To the best of our knowledge, the immersion results for quaternionic flag manifolds have not been given before in the literature.…”