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October, 2012 The intersection of two real forms in Hermitian symmetric spaces of compact type
Makiko Sumi TANAKA, Hiroyuki TASAKI
J. Math. Soc. Japan 64(4): 1297-1332 (October, 2012). DOI: 10.2969/jmsj/06441297

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.

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Makiko Sumi TANAKA. Hiroyuki TASAKI. "The intersection of two real forms in Hermitian symmetric spaces of compact type." J. Math. Soc. Japan 64 (4) 1297 - 1332, October, 2012. https://doi.org/10.2969/jmsj/06441297

Information

Published: October, 2012
First available in Project Euclid: 29 October 2012

zbMATH: 1260.53107
MathSciNet: MR2998924
Digital Object Identifier: 10.2969/jmsj/06441297

Subjects:
Primary: 53C40
Secondary: 53D12

Rights: Copyright © 2012 Mathematical Society of Japan

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Vol.64 • No. 4 • October, 2012
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