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Invariant Kähler metrics and projective embeddings of the flag manifold

  • Kichoon Yang (a1)
Abstract

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.

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[1]A. Borel , ‘Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts’, Ann. of Math. 57 (1953), 115207.

[2]M. Goto , ‘On algebraic homogeneous spaces’, Amer. J. Math. 76 (1954), 811–313.

[3]H.C. Wang , ‘Closed manifolds with homogeneous complex structure’, Amer. J. Math. 76 (1954), 132.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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