International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 8, Pages 453-469
doi:10.1155/S0161171202012115
An introduction to spherical orbit spaces
Jill McGowan1
and Catherine Searle2
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
Abstract
Consider a compact, connected Lie group G acting isometrically on a sphere Sn of radius 1. Two-dimensional quotient spaces of the type Sn/G 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.