Нормалност на туисторното пространство на 5-мерно многообразие с неприводима SО(3)-структура

[Davidov Johann; Давидов Йохан] A manifold with an irreducible SО(3)-structure is a 5-manifold M whose structure group can be reduced to the group SО(3), non-standardly imbedded in SО(5). The study of such manifolds has been initiated by M. Bobieński and P. Nurowski who, in particular, have shown that one can define four СR-structures on a twistor-like 7-dimensional space associated to 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 condition for normality in geometric terms of the base manifold M. Examples illustrating this result are presented at the end of the paper. 2000 Mathematics Subject Classification: 53C28; 53D15; 53B15.