HOME > Table of Contents and Abstracts > Vol. 62, No. 3
Tohoku Mathematical Journal
SECOND SERIES VOL. 62, NO. 3
|Tohoku Math. J.|
62 (2010), 375-382
THE INTERSECTION OF TWO REAL FORMS IN THE COMPLEX HYPERQUADRIC
(Received November 12, 2009, revised March 1, 2010)
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.
To the top of this page
Back to the Contents