International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 8, Pages 453-469
An introduction to spherical orbit spaces
1Department of Mathematics, Howard University, Washington 20059, DC, USA
2Instituto de Mathemáticas de la UNAM, Unidad Cuernavaca, Avenida Universidad S/N, Colonia lo Mas de Chamilpa, Cuernavaca 62210, Morelos, Mexico
Received 21 February 2001; Revised 24 September 2001
Copyright © 2002 Jill Mcgowan and Catherine Searle. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Consider a compact, connected Lie group acting isometrically on a sphere of radius . Two-dimensional quotient spaces of the type have been investigated extensively. This paper provides an elementary introduction, for nonspecialists, to this important field by way of several classical examples and supplies an explicit list of all the isotropy subgroups involved in these examples.