## Journal of the Mathematical Society of Japan

### The intersection of two real forms in Hermitian symmetric spaces of compact type

#### Abstract

We show that the intersections of two real forms, certain totally geodesic Lagrangian submanifolds, in Hermitian symmetric spaces of compact type are antipodal sets. The intersection number of two real forms is invariant under the replacement of the two real forms by congruent ones. If two real forms are congruent, then their intersection is a great antipodal set of them. It implies that any real form in Hermitian symmetric spaces of compact type is a globally tight Lagrangian submanifold. Moreover we describe the intersection of two real forms in the irreducible Hermitian symmetric spaces of compact type.

#### Article information

Source
J. Math. Soc. Japan, Volume 64, Number 4 (2012), 1297-1332.

Dates
First available in Project Euclid: 29 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1351516776

Digital Object Identifier
doi:10.2969/jmsj/06441297

Mathematical Reviews number (MathSciNet)
MR2998924

Zentralblatt MATH identifier
1260.53107

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

#### Citation

TANAKA, Makiko Sumi; TASAKI, Hiroyuki. The intersection of two real forms in Hermitian symmetric spaces of compact type. J. Math. Soc. Japan 64 (2012), no. 4, 1297--1332. doi:10.2969/jmsj/06441297. https://projecteuclid.org/euclid.jmsj/1351516776

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