On the topology and the geometry of SO(3)-manifolds
Abstract
Consider the nonstandard embedding of SO(3) into SO(5) given by the 5-dimensional irreducible representation of SO(3), henceforth called SO(3). In this note, we study the topology and the differential geometry of 5-dimensional Riemannian manifolds carrying such an SO(3) structure, i.\,e. with a reduction of the frame bundle to SO(3).
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