The involutions of compact symmetric spaces. III
type: Item
instance of: scholarly article
title: The involutions of compact symmetric spaces. III
zbMATH Open document ID: 0836.53033
author: Tadashi Nagano
author: Makiko S. Tanaka
published in: Tokyo Journal of Mathematics
publication date: 1996-04-16T00:00:00Z
review text: This article is a continuation of the papers of the first author [for part I see: ibid. 11, No. 1, 57-79 (1988; Zbl 0655.53041); for part II see: ibid. 15, No. 1, 39-82 (1992; Zbl 0779.53036)]. Here the authors construct certain fibrations coming from symmetric spaces, which are useful for the study of Riemannian submersions. Their base manifolds are polars and the fibres are ``centrioles of the meridians''. (These concepts always make sense in a compact symmetric space and they are recalled in the first chapter.) One of the main results is the explicit classification of the fibrations in question -- they include as examples various twistor spaces by Calabi, Penrose and others. As an application, a classification of special graded algebras by S. Kaneyuki is described in an alternative way, providing more geometrical insight.
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 821722
zbMATH Keywords: fibration
zbMATH Keywords: graded Lie algebra
zbMATH Keywords: twistor structure
zbMATH Keywords: compact symmetric space
reviewed by: Oldřich Kowalski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270043621
OpenAlex ID: W4210337306
DOI: 10.3836/TJM/1270043621
description: scientific article; zbMATH DE number 821722