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On the topology and the geometry of SO(3)-manifolds

On the topology and the geometry of SO(3)-manifolds,10.1007/s10455-010-9245-x,Annals of Global Analysis and Geometry,Ilka Agricola,Julia Becker-Bender

On the topology and the geometry of SO(3)-manifolds  
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Consider the non-standard embedding of SO(3) into SO(5) given by the five-dimensional irreducible representation of SO(3), henceforth called SO(3)ir. In this note, we study the topology and the differential geometry of five-dimensional Riemannian manifolds carrying such an SO(3)ir structure, i.e., with a reduction of the frame bundle to SO(3)ir.
Journal: Annals of Global Analysis and Geometry - ANN GLOB ANAL GEOM , vol. 40, no. 1, pp. 67-84, 2011
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