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Invariant Kähler metrics and projective embeddings of the flag manifold

Published online by Cambridge University Press:  17 April 2009

Kichoon Yang
Department of Mathematics ArkansasState University State University, AR 72467United States of America
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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.

Research Article
Copyright © Australian Mathematical Society 1994


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