Year: 1949
Type: article
Abstract: The present note pertains principally to two papers of D. Montgomery and H. Samelson [l, 2J, 1 in which the authors study compact Lie groups transitive on tori [l] and spheres [2], I will here prove in another way, generalize, and sharpen a part of their results.§1 contains the remarks to [l], §2 to [2]; they are independent of one another and the methods used in both are quite different.I recall first the definition and some simple properties of homogeneous spaces.A manifold W is a homogeneous space under the Lie group 2 G if to each element a of G there corresponds a differentiate transformation T a 'x-^T a (x)of W into itself such that: (1) T a {x) depends continuously on the pair a£G, x£:W.(2) To the product (ab) corresponds the mapping x->T Ca b) (x)
Author: Armand Borel
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2054095663