## Tohoku Mathematical Journal

### The intersection of two real forms in the complex hyperquadric

Hiroyuki Tasaki

#### 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 62, Number 3 (2010), 375-382.

Dates
First available in Project Euclid: 15 October 2010

https://projecteuclid.org/euclid.tmj/1287148617

Digital Object Identifier
doi:10.2748/tmj/1287148617

Mathematical Reviews number (MathSciNet)
MR2742014

Zentralblatt MATH identifier
1204.53046

Subjects
Secondary: 53D12: Lagrangian submanifolds; Maslov index

#### Citation

Tasaki, Hiroyuki. The intersection of two real forms in the complex hyperquadric. Tohoku Math. J. (2) 62 (2010), no. 3, 375--382. doi:10.2748/tmj/1287148617. https://projecteuclid.org/euclid.tmj/1287148617

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