A duality between compact symmetric triads and semisimple pseudo-riemannian symmetric pairs with applications to geometry of hermann type actions

Kurando Baba, Osamu Ikawa, Atsumu Sasaki

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Abstract

This is a survey paper of not-yet-published papers listed in the reference as [1–3]. We introduce the notion of a duality between commutative compact symmetric triads and semisimple pseudo-Riemannian symmetric pairs, which is a generalization of the duality between compact/noncompact Riemannian symmetric pairs. As its application, we give an alternative proof for Berger’s classification of semisimple pseudo-Riemannian symmetric pairs from the viewpoint of compact symmetric triads. More precisely, we give an explicit description of a one-to-one correspondence between commutative compact symmetric triads and semisimple pseudo-Riemannian symmetric pairs by using the theory of symmetric triads introduced by the second author. We also study the action of a symmetric subgroup of G on a pseudo-Riemannian symmetric space G/H, which is called a Hermann type action. For more details, see [1–3].

Original languageEnglish
Title of host publicationHermitian-Grassmannian Submanifolds
EditorsYoshihiro Ohnita, Jiazu Zhou, Byung Hak Kim, Hyunjin Lee, Young Jin Suh
PublisherSpringer New York LLC
Pages211-221
Number of pages11
ISBN (Print)9789811055553
DOIs
Publication statusPublished - 2017
Event20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, IWHSSS 2016 - Daegu, Korea, Republic of
Duration: 26 Jul 201630 Jul 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume203
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, IWHSSS 2016
Country/TerritoryKorea, Republic of
CityDaegu
Period26/07/1630/07/16

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