The involutions of compact symmetric spaces. III
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.
scientific article; zbMATH DE number 821722