Global aspects of spontaneous compactification

Abstract

The well known Freund-Rubin 'spontaneous compactification' mechanism (1980) is based on Myers' theorem in global differential geometry. The authors extend this observation and attempt to clarify various global questions connected with the Freund-Rubin mechanism. The recent suggestion that non-compact manifolds of finite volume be employed as models of internal spaces is then considered. A non-compact analogue of the Freund-Rubin mechanism is proposed.