TY - GEN

T1 - A duality between compact symmetric triads and semisimple pseudo-riemannian symmetric pairs with applications to geometry of hermann type actions

AU - Baba, Kurando

AU - Ikawa, Osamu

AU - Sasaki, Atsumu

N1 - Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2017.

PY - 2017

Y1 - 2017

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=85030169544&partnerID=8YFLogxK

U2 - 10.1007/978-981-10-5556-0_18

DO - 10.1007/978-981-10-5556-0_18

M3 - Conference contribution

AN - SCOPUS:85030169544

SN - 9789811055553

T3 - Springer Proceedings in Mathematics and Statistics

SP - 211

EP - 221

BT - Hermitian-Grassmannian Submanifolds

A2 - Ohnita, Yoshihiro

A2 - Zhou, Jiazu

A2 - Hak Kim, Byung

A2 - Lee, Hyunjin

A2 - Jin Suh, Young

PB - Springer New York LLC

T2 - 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, IWHSSS 2016

Y2 - 26 July 2016 through 30 July 2016

ER -