The intersection of two real flag manifolds in a complex flag manifold

2025/07/17 by Osamu Ikawa, Ikawa, Osamu, Hiroshi Iriyeh +7 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Data Management and Algorithms #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2507.12785

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.

Citations

• Double Satake diagrams and canonical forms in compact symmetric triads
• Lagrangian Floer homology of a pair of real forms in Hermitian symmetric\n spaces of compact type
• The kinematic formula in Riemannian homogeneous spaces

Cited by

• Polars and antipodal sets of generalized s-manifolds

Related

• Flag structures on real 3-manifolds
• An example of a domain in a complex flag manifold
• Levi-Civita connections of flag manifolds
• Orbits of real forms in complex flag manifolds
• Flag Manifolds and Grassmannians