The intersection of two real forms in the complex hyperquadric
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We show that, in the complex hyperquadric, the intersection of two real forms, which are certain totally geodesic Lagrangian submanifolds, is an antipodal set whose cardinality attains the smaller 2-number of the two real forms. As a corollary of the result, we know that any real form in the complex hyperquadric is a globally tight Lagrangian submanifold.
- Tohoku Math. J.
Tohoku Math. J. 62, 375-382, 2010