Journal of the Mathematical Society of Japan

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

Makiko Sumi TANAKA and Hiroyuki TASAKI

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Abstract

We minutely describe the intersection of two real forms in a non-irreducible Hermitian symmetric space $M$ of compact type. In the case where $M$ is irreducible we have already done it in our previous paper. In this paper we reduce the description of the intersection of two real forms to that in some special cases. This reduction is based on the information of the group of all isometries obtained by Takeuchi. We can describe the intersection in the special cases and in all cases. In particular we obtain the intersection number of two real forms in a Hermitian symmetric space of compact type.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 1 (2015), 275-291.

Dates
First available in Project Euclid: 22 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1421936553

Digital Object Identifier
doi:10.2969/jmsj/06710275

Mathematical Reviews number (MathSciNet)
MR3304022

Zentralblatt MATH identifier
1335.53068

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

Keywords
real form Hermitian symmetric space antipodal set

Citation

TANAKA, Makiko Sumi; TASAKI, Hiroyuki. The intersection of two real forms in Hermitian symmetric spaces of compact type II. J. Math. Soc. Japan 67 (2015), no. 1, 275--291. doi:10.2969/jmsj/06710275. https://projecteuclid.org/euclid.jmsj/1421936553


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References

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