A class of totally geodesic foliations of Lie groups
type: Item
instance of: scholarly article
title: A class of totally geodesic foliations of Lie groups
zbMATH Open document ID: 0701.53054
DOI: 10.1007/BF02881115
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1990-01-01T00:00:00Z
review text: Let G be a compact, connected, simply-connected Lie group, and let K be a connected closed subgroup of G such that G/K is a rank-1 Riemannian symmetric space. This paper is devoted to classifying the foliations of G with leaves of the form \(gKh^{-1}\). In the case when \(G/K=S^ n\), the homotopy type of the space of such foliations is also given. This work generalizes that of \textit{H. Gluck} and \textit{F. W. Warner} [Duke Math. J. 50, 107-132 (1983; Zbl 0523.55020)] concerning the great circle fibrations of the three sphere.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4149097
zbMATH Keywords: cutlocus
zbMATH Keywords: Lie group
zbMATH Keywords: symmetric space
zbMATH Keywords: foliations
Wikidata QID: Q115391319
author: Gopalkrishnan Santhanam
MaRDI profile type: Publication
cites work: Great circle fibrations of the three-sphere
cites work: Q3897665
description: scientific article; zbMATH DE number 4149097