a1 Department of Mathematics Arkansas State University State University, AR 72467 United States of America
We determine explicitly the space of invariant Hermitian and Kähler metrics on the flag manifold. In particular, we show that a Killing metric is not Kähler. 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.
(Received April 05 1993)