The intersection of two real flag manifolds in a complex flag manifold
Differential Geometry
2025-07-18 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2507.12785,
title = {The intersection of two real flag manifolds in a complex flag manifold},
author = {Osamu Ikawa and Hiroshi Iriyeh and Takayuki Okuda and Takashi Sakai and Hiroyuki Tasaki},
journal= {arXiv preprint arXiv:2507.12785},
year = {2025}
}
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27 pages