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<p>We give a necessary and sufficient condition for two real flag manifolds, which are not necessarily congruent, in a complex flag manifold to intersect transversally in terms of the symmetric triad. Then we show that the intersection of two real flag manifolds is antipodal. As an application, we prove that any real flag manifold in a complex flag manifold is a globally tight Lagrangian submanifold.</p>

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The Intersection of Two Real Flag Manifolds in a Complex Flag Manifold

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月10日

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  • Osamu Ikawa,
  • Hiroshi Iriyeh,
  • Takayuki Okuda,
  • Takashi Sakai,
  • Hiroyuki Tasaki

摘要

We give a necessary and sufficient condition for two real flag manifolds, which are not necessarily congruent, in a complex flag manifold to intersect transversally in terms of the symmetric triad. Then we show that the intersection of two real flag manifolds is antipodal. As an application, we prove that any real flag manifold in a complex flag manifold is a globally tight Lagrangian submanifold.