Tohoku Mathematical Journal
2010
September
SECOND SERIES VOL. 62, NO. 3

Tohoku Math. J.
62 (2010), 375-382

Title THE INTERSECTION OF TWO REAL FORMS IN THE COMPLEX HYPERQUADRIC

Author Hiroyuki Tasaki

(Received November 12, 2009, revised March 1, 2010)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 53C40; Secondary 53D12.
Key words and phrases. Real form, Lagrangian submanifold, complex hyperquadric, antipodal set, 2-number, globally tight.

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