Tohoku Mathematical Journal

The intersection of two real forms in the complex hyperquadric

Hiroyuki Tasaki

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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.

Article information

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

First available in Project Euclid: 15 October 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53D12: Lagrangian submanifolds; Maslov index

Real form Lagrangian submanifold complex hyperquadric antipodal set 2-number globally tight


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.

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