Normality of the Twistor Space of a 5-Manifold with an Irreducible SO(3)-Structure

Abstract

A manifold with an irreducible SO(3)-structure is a 5-manifold M whose structure group can be reduced to the group SO(3), non-standardly imbedded in SO(5). The study of such manifolds has been initiated by Bobienski and Nurowski who, in particular, have shown that one can define four CR-structures on a twistor-like 7-dimensional space associated with M. In the present paper, it is observed that these CR-structures are induced by almost contact metric structures. The purpose of the paper is to study the problem of normality of these structures. The main result gives necessary and sufficient conditions for normality in geometric terms of the base manifold M. Examples illustrating this result are presented at the end of the paper.