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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
Kichoon Yang
Affiliation:
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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 2 , April 1994 , pp. 239 - 247
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Borel, A., ‘Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts’, Ann. of Math. 57 (1953), 115–207.CrossRefGoogle Scholar
[2]Goto, M., ‘On algebraic homogeneous spaces’, Amer. J. Math. 76 (1954), 811–313.CrossRefGoogle Scholar
[3]Wang, H.C., ‘Closed manifolds with homogeneous complex structure’, Amer. J. Math. 76 (1954), 1–32.CrossRefGoogle Scholar