Invariant Kähler metrics and projective embeddings of the flag manifold

Kichoon Yang
1994 Bulletin of the Australian Mathematical Society  
We determine explicitly the space of invariant Hermitian and Kahler metrics on the flag manifold. In particular, we show that a Killing metric is not Kahler. The Chern forms are also computed in terms of the Maurer-Cartan form, and this calculation is used to prove that the flag manifold is projective algebraic. An explicit projective embedding of the flag manifold is also given.
doi:10.1017/s0004972700016300 fatcat:wa56yd5h4zhevm33c7cnhxl5y4