2013/05/21 by Johann Davidov, Davidov, Johann
Mathematics · #53B15 #53C28 #53D15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1305.4882
openalex publication_date 2013/05/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
A manifold with an irreducible SO(3)-structure is a 5-manifold M whose\nstructure group can be reduced to the group SO(3), non-standardly imbedded in\nSO(5). The study of such manifolds has been initiated by M. Bobie 'nski and\nP. Nurowski who, in particular, have shown that one can define four\nCR-structures on a twistor-like 7-dimensional space associated to M. In\nthe present paper it is observed that these CR-structures are induced by\nalmost contact metric structures. The purpose of the paper is to study the\nproblem of normality of these structures. The main result gives necessary and\nsufficient condition for normality in geometric terms of the base manifold M.\nExamples illustrating this result are presented at the end of the paper.\n